25
\$\begingroup\$

The objective

Given the non-negative integer \$n\$, output the value of the hyperfactorial \$H(n)\$. You don't have to worry about outputs exceeding your language's integer limit.

Background

The hyperfactorial is a variant of the factorial function. is defined as $$ H(n) = 1^{1} \cdot 2^{2} \cdot 3^{3} \cdot \: \cdots \: \cdot n^{n} $$

For example, \$H(4) = 1^{1} \cdot 2^{2} \cdot 3^{3} \cdot 4^{4} = 27648\$.

Test cases

n   H(n)
0   1
1   1
2   4
3   108
4   27648
5   86400000
6   4031078400000
7   3319766398771200000
8   55696437941726556979200000

Rules

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2
  • \$\begingroup\$ I think one might be able to write a competitive 4 bit assembler (or even 8 bit assembler) answer which is a tiny LUT. \$\endgroup\$
    – abligh
    Oct 5, 2021 at 2:40
  • \$\begingroup\$ oeis.org/A002109 \$\endgroup\$
    – bigyihsuan
    Nov 14, 2022 at 19:32

77 Answers 77

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1
2 3
14
\$\begingroup\$

Jelly, 3 bytes

*)P

Try it online!

How it works

*)P - Main link. Takes n on the left
 )  - Over each integer 1 ≤ i ≤ n:
*   -   Raise i to the power i
  P - Product
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5
  • \$\begingroup\$ I will accept this answer since it appears to be the shortest. \$\endgroup\$
    – Nirvana
    Oct 4, 2021 at 15:52
  • 10
    \$\begingroup\$ @Nirvana I appreciate that. However, 8 hours is far too short to accept a winner, as it often indicates (unofficially) that the challenge is over. If I accept a winner, I usually wait a minimum of 3 days so that everyone has time to see the challenge. Additionally, we discourage accepting an answer on pure [code-golf] challenges, as we consider these challenges to be competitions within languages (e.g. Jelly vs Jelly, rather than Jelly vs Java), and accepting an answer contradicts that. It's entirely up to you if you'd like to follow that convention however. \$\endgroup\$
    – caird coinheringaahin g ♦
    Oct 4, 2021 at 17:15
  • \$\begingroup\$ Jelly will still be the winner, 3 bytes is damn short \$\endgroup\$
    – Wasif
    Oct 4, 2021 at 17:55
  • 3
    \$\begingroup\$ Tied with Gaia now. \$\endgroup\$
    – Adám
    Oct 4, 2021 at 20:38
  • \$\begingroup\$ @cairdcoinheringaahing see, and THAT is why we have the occasional "ban golflangs" thread on meta - you can say how things should be and stuff but this is reality \$\endgroup\$
    – htmlcoderexe
    Oct 6, 2021 at 14:00
9
\$\begingroup\$

Wolfram Language (Mathematica), 19 bytes

Product[n^n,{n,#}]&

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also as @att mentioned there is a built-in for this...

Wolfram Language (Mathematica), 14 bytes

Hyperfactorial

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1
  • 1
    \$\begingroup\$ The built-in Hyperfactorial is 14 bytes \$\endgroup\$
    – att
    Oct 4, 2021 at 19:27
8
\$\begingroup\$

APL (Dyalog Classic), 5 bytes

⍳×.*⍳

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Monadic fork train

First it evaluates range of the input, and dots the power and takes the product.

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2
  • 3
    \$\begingroup\$ While not as nice looking, ×.*⍨⍳ would be more efficient. \$\endgroup\$
    – Adám
    Oct 5, 2021 at 5:36
  • \$\begingroup\$ @Adám nice, i wasn't aware of this use of commute \$\endgroup\$
    – Wasif
    Oct 8, 2021 at 9:19
8
\$\begingroup\$

Gaia, 3 bytes

*†Π

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† vectorizes the operator on its left, integer arguments are implicitly cast to ranges. * is exponentiation and Π the product of a list.

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\$\endgroup\$
6
\$\begingroup\$

JavaScript (ES7), 20 bytes

f=n=>n?n**n*f(n-1):1

Try it online!

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6
\$\begingroup\$

Python 3, 28 bytes

f=lambda n:n<1or n**n*f(n-1)

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6
\$\begingroup\$

Nibbles, 2 bytes

$*@^

Note that this problem influenced how nibbles decides to use implicit args from implicit ops. I'm currently thinking of getting rid of implicit fold since it is uncommonly used though.

     # implicit fold since accumulator is used
     # implicit range from 1 since there's things after an integer 
$    # first input integer
 *   # mult
  @  # accumulator from fold
   ^ # exponentiation
     # implicit $ since need another arg to ^
     # implicit $ since need another arg to ^
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\$\endgroup\$
5
\$\begingroup\$

tinylisp, 51 bytes

(load library
(d H(q((N)(i N(*(pow N N)(H(dec N)))1

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Ungolfed

(load library)            ; for *, pow, and dec

(def hyper                ; name something
  (lambda (n)             ; a lambda function that takes one parameter n
    (if n                 ; if n...   
      (*                  ; ...is non-zero, multiply...
        (pow n n)         ; ...n raised to itself...
        (hyper (dec n)))  ; by the hyperfactorial of n-1
      1)))                ; otherwise if n is zero, return 1
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\$\endgroup\$
1
  • 1
    \$\begingroup\$ 50 bytes non-recursive solution \$\endgroup\$
    – Giuseppe
    Feb 3, 2022 at 13:22
4
\$\begingroup\$

Husk, 5 bytes

Πm´^ḣ

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Π       # product of
 m      # mapping across all values of
     ḣ  # 1..input
  ´^    # x to the power of x
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\$\endgroup\$
4
\$\begingroup\$

R, 20 bytes

prod((x=1:scan())^x)

Try it online!

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\$\endgroup\$
4
\$\begingroup\$

Haskell, 20 bytes

h 0=1
h n=n^n*h(n-1)

Try it online!

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\$\endgroup\$
4
\$\begingroup\$

jq, 42 bytes

[range(.+1)]|reduce.[]as$i(1;.*pow($i;$i))

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1
  • \$\begingroup\$ You can simplify the [range]|reduce.[] to reduce(range(.+1))as$i to save 4 bytes] \$\endgroup\$
    – Sara J
    Oct 6, 2021 at 18:27
4
\$\begingroup\$

Java (JDK), 51 bytes

n->{var r=1;for(;n>0;)r*=Math.pow(n,n--);return r;}

Try it online!

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4
\$\begingroup\$

TI-Basic, 19 17 14 bytes

prod(seq(I^I,I,1,Ans+not(Ans

sadly 0^0 or an empty list errors, so 0 has to be turned into 1

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4
\$\begingroup\$

Factor + math.factorials, 15 bytes

hyper-factorial

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Built-in.

Factor + math.unicode, 33 27 bytes

[ [1,b] [ dup ^n ] map Π ]

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This could have been 26 bytes, but ^ returns NaN for 0^0. Factor is the only language I know of that doesn't just return 1 for that. So I had to use ^n instead, which is a helper word used to implement ^ that hasn't been 'fixed' yet.

  • [1,b] A range from 1 to whatever is on top of the data stack, inclusive.
  • dup ^n Raise an integer to itself.
  • [ ... ] map Apply a quotation to each element of a sequence, collecting the results in a new sequence of the same length.
  • Π Product of a sequence.
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1
  • 1
    \$\begingroup\$ You can add Mathematica to that list :) \$\endgroup\$
    – att
    Oct 5, 2021 at 19:59
4
\$\begingroup\$

Kotlin, 59 bytes

fun h(i:Double):Double=if(i<1)1.0 else Math.pow(i,i)*h(i-1)

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Longest submission yet, but thought I might as well give Kotlin a shot. Used the = format for functions to eliminate 2 brackets as well as the return.

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\$\endgroup\$
1
  • 2
    \$\begingroup\$ Welcome to Code Golf! Nice answer! \$\endgroup\$
    – Rydwolf Programs
    Oct 4, 2021 at 18:46
3
\$\begingroup\$

C (gcc), 28 bytes

H(n){n=n?pow(n,n)*H(--n):1;}

Try it online!

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3
\$\begingroup\$

Wren, 43 bytes

var F=Fn.new{|n|n<1?1:n.pow(n)*F.call(n-1)}

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Alternate:

Wren, 44 bytes

Fn.new{|n|(1..n).reduce(1){|a,b|a*b.pow(b)}}

Try it online!

Improve this answer
\$\endgroup\$
1
  • \$\begingroup\$ wow reminds me a lot of rust \$\endgroup\$
    – don bright
    Oct 5, 2021 at 4:33
3
\$\begingroup\$

Vyxal, 4 bytes

ɾ:eΠ

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Obligatory answer

ɾ              # Range
:              # Dup
e             # Power
Π            # Product
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\$\endgroup\$
3
\$\begingroup\$

dc, 24 bytes

?[1+[d1-d1<xr1-d^*]dsxxp

Explanation

This is a complete program, that reads input from stdin and writes the result to stdout.

?                       # input
1+                      # avoid H(-1)
[                       # function x
  d1-                   # 
  d1<x                  # recurse       : n n-1 ... i+1 H(i-1)
  r1-                   #               : n n-1 ... H(i-1) i
  d^*                   #               : n n-1 ... H(i)
]dsxx                   # define and execute
p                       # output

Output

H(n) for n = 0..12

0
1
4
108
27648
86400000
4031078400000
3319766398771200000
55696437941726556979200000
21577941222941856209168026828800000
215779412229418562091680268288000000000000000
61564384586635053951550731889313964883968000000000000000
548914237009501581804104224704637116078267727827959808000000000000000

My machine takes almost 0.7 seconds to compute H(200), but it does produce the correct result:

114256002424540571298977792354054343003217988447353197803701128087779\
727310773544883222069862169886712875089569689613436517195625058699339\
831616247967378727547253765461789388643475674400611735920545310021028\
378006078740483920058608872101517118552137511462765664553099379243826\
960171887170750794198373595289872526218671094534622811250467573078955\
097722440499909299236803909456886903559422482755722874996888761181995\
575299415208051459908113833797191408981585936952677202993799475038316\
559629150663378834397372775965856682894873495939410259095804412984759\
376802645433107086846121910224544820403394942396165166503784543183923\
373316267239065885057694972898540625272750046246522113004186914354002\
967536413371473458112220769020094756837578527902012213205896270144393\
863599279497755781359466901673079326909202551645285985747551170700716\
842425698975536766498808553756048408306339794216494138288030784286578\
757511579359563917784149939178533514638276262178221710320662541522716\
166268310550789650887610134719729891484651131282509122835031254510412\
859215509732637002095449585308892098589802359045914197581197309643963\
042570582527203047381981490652454323893038445041694758990588984561508\
024977520153869302479414855203541538559245994267482585355022642863859\
784222422005021616964777696793772349735028255170680455712484791660880\
381133647422166704047722699070109094074510187247343055332257496929374\
982064491045838594959100552218107373079642910265887514107042314387137\
231583168255471546888411138370063211060324585902513206145493958317539\
840648935101056767774783896580016743810934173275647035655085909723344\
400585286826414068777563965071196389690941135698863589037499407785370\
931798703443963281315725441703395909623807818562899480337755459429222\
263976154559801703132418440141220192063353095047779835936440544198953\
496106173470542538936478118001519398934406367850808122800102137273226\
951723289344106737093183594520201847490204826536442751006791251960765\
409736570349501810834880546030444722460505622335562771218876927864732\
533831989277488466279926764165356648286028875357501991394907871736473\
399337480995325006099531629623628775557151039011468601336589825839738\
631718648726576082486937471392562052316112813773965598704019732181766\
979636498126699138316658703065343361486555049963171513229287190102366\
294038070909517003192684859103788524924734600167422726737999487560861\
040910125441478016464932490390352767808126453168977619717961242515337\
678589841167345358713873500430963639031923908700261694508782150681050\
006111529466925629252138641356979249757548377531461415227595617743646\
019706623647306680452085764528828628378729906162793797766057848324098\
880977726680150730390074716141211796155230858668012021940942979991319\
892197094655756666501455192326506825509530719155451676296396102560013\
841584265351485313695020472184192704099107932797640710173835532960606\
518538605516574602321430208034314359982648827905481627199797808702727\
344458806167205608568625797981988480548489292548067131307825217362115\
487277151573038609637079476077578954700658210221211043513144482137132\
113794287001433270940578127570053434695653912547579202493901871464470\
764410974150819235945558607363556467922279391141836922743541233760821\
871365085257243448039467666652724537269128483841450819722610910449669\
667767218934240840176992473839442233550613463850853485560398554469357\
611537501209062167152021399590356213475289096528949653047033419077429\
299028564676171187099901772701404490557158793484243417114875079809449\
627812693323373523747772814832161656651663374496734064538978915783865\
719064174822864696226655708942852177545994665514849721267519945794503\
019098476165255673401283399976325921222555982464845071082560857852257\
814145566478967899059920204170727945409097495154492869672134459786294\
588119159908191561922643839816897827104225462279731830827250471252105\
289727169676968836275320004859466161656331082081074381176816967370602\
357442772694553727911750007625712888624429904817070697897964886832493\
345528030314492840383966128843659735252693645758721744757267671336699\
697149807573431757428427239466529780150411631632066022100098544057533\
387989402082327607683479023952713064900546185006785478600337149539296\
663361814407606344949829339294479920368454331595871231338484805775737\
339268396124977267103545541977669058589689418363091692719790628856414\
752071432633359549389607990792617571221154257026279901828952182073374\
160861868734416746968494659933958156742463652295106500468210780119125\
220209380290875380832470409648848082808663586942813054685601333888677\
903229796350639694587698272283080314334773653111218034106708436851163\
056715554656438061557864316343565021443951504379532417965485201636186\
463813912432724675905548790267512971651098333554063940806626704854532\
678674167073399666603479497096163139406079292169446126287164855437310\
733645103657687054384245612640135453530729419221334723538721255762469\
348656691594173954864816605371367857438364854545334435452281244641153\
702780834293385080202596856941397712010881729069210455124793116543955\
764287224835926198843406678698041913931641907309743017824157088832657\
515931712589921404995250184506019056203133181617154100069201866951525\
300872664323283710970049931600220543834155799207559964184227001086729\
978318247276684554857576596547291291791522751007585853793360225113135\
450501518599762144278325251060114811491521595770223299394208499421070\
133134002376834102080109021979719187115415860089714599508435221834288\
106979134790461271826466644755668937746875390891835581995388195707703\
666919259484508094626586130500902421761233473185812236823727560637765\
353284587005782503482049179577624131003496831794473409129318251405306\
686312023625090599797707676764002997295491901065845799891148513188011\
750255365930732717166438760960930254270355434958193721008813937013342\
442685357933848612269061232591941511207731095268816549202309436856983\
863709498625968309204249579255954213842990272453525630818763597799543\
593087313268427793519216838584166922708627220843209392429847694078662\
627081045478537054881042974186251081449455396030353464966077751989172\
967094495553235926368816821576526232804884953832820814720565106292278\
677023212354425827714341638534116865568614053180685437672841412518894\
098874469347176584909301684501882789675804879960815875737873223894302\
068322229857523890186183543936935430404240034004709340156823935334504\
280773088422757352262015925135936299428100399162508993701323816640249\
317502708643002177380916843121414525377166307214659890456197078789358\
755908958395704605757659385312957851526639927217127812638621838046618\
256249655670855709886714485145533985086443137064765377391996261567764\
614649944571049532129160422595979803302687452962711606329612008212827\
794401494192040770665411078681415279435060816655175330979102977082874\
632330444354061833803759173996116082517816249241467318683953133297949\
696966800597273657946143827878859661836812064102045501830604467916228\
427069899293175548188750078304435399590540700476604483395383697312578\
097710820312329606242276447140831589400706797160881537904137892646388\
261066966454548869342350130453494223912785614903507340787315001904795\
688540272824396638149906352594040357284385938277509795452746883194274\
390009993333838096016899929412160162615538212444522338199878096100853\
638701901085648519985630176886727084180895587065782329076867465210575\
281386375663556976026065633532489743239889186305075304808560243262432\
658085969412020827902073591982408638009516334902222599715386120602437\
678310010096587347186053193158239648969456170841664624039286167247669\
514436308002065354268316000349861095951926759431651589488622884486382\
277854033455441602586071384379537383305706042265499575026224506704860\
688406915452474511683218154440889210555179680616817271305312473155544\
143262273531331795805472254371401019589348634412412286987413907792718\
329915124784729596566415082748529970796499261705982501268401723583887\
701661443797764811659857704733113125011378104100970585073283674392976\
859476816730766230843992524449084734798618995888731548845560723062966\
192859122943220390909175950182057052843622022554828023378885550828117\
382718195394157370910647482474167099695486548360631460470999045477378\
132717331452335714187924997815103638622262298849924210205241176668405\
490741524219253278664341011210099915988552406343854573062664870584245\
103886217277906440977065037168659090059763288778505082007530932618466\
494869181704099810631362022702089755491800061458537467852967380851010\
908862739733011423332473338496528317600181547938903583970178021411350\
504107353290656971578124200774189092891257270280529095290550988723728\
135603533746551804333320307013973767695324099720923379543683864817974\
710553868201698590292895333412491357784173524677821074492989035878523\
065616904294807445990638805797254482102285949882214670841897742949328\
311659987640881568459282440548451135162773664037389258355421285035420\
999699985577663763700005757941427315733197266168699581396576204803981\
473126870934075898120336661598190205939756443947057710182924789850055\
001425654550118743113257624420824183938997656885814673594734917916409\
078995498945642404630814171603046441105445059249548610322842910754951\
846627795460490833776103956049657955540015291032378840531042472594532\
860423319860149058941766354088020712438608204454072807575885575852839\
180700772630347090579280688794361068997524503617691544202365939291565\
645671286667544529026174876789733907296960576178709446195376983454472\
164584703777117244823990537583736958740841562740244004026203727555258\
450538750500484541128688250020648123312909872053878444932137569761105\
646598390520596957373979148797644934213546809772428508682350740007209\
819026797315661258929751889448192710982091237434909749464078055542925\
758110822533573122134535676028907089176208169078890508131338313078120\
366292092748543956445763451239618092200751801948183924253225759130045\
402864771211838018815605401626689028050384789832787839775255721097218\
181110343132212865937413848154233885501099705968645937079387543236067\
419341630111614913910492435024464166688710987099886511583318895948003\
248879615736644901850078099348201377864691386256283320069993735388706\
880978227943386880372348195108338420348643722382324037845214076409223\
421605406326543434017961739452074663199250414741826344527959432512472\
288051981715822955586322044373144003885900746941921709703799672502350\
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Larger values work fine, but exceed the maximum answer size allowed here.

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1
  • \$\begingroup\$ I followed the advice in the question not to worry about outputs exceeding the language's integer limit. ;-) \$\endgroup\$
    – Toby Speight
    Oct 28, 2021 at 16:22
3
\$\begingroup\$

Scala, 40 38 bytes (supporting Big Integers)

1.to(_).map(x=>BigInt(x)pow x).product

Provides exact results up to crazy large numbers with several billions of digits, namely up to Hyperfactorial(2^31-1).

Saved 2 bytes thanks to @user.

Try it online!

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1
  • 1
    \$\begingroup\$ Nice, you can do BigInt(x)pow x to save a couple bytes \$\endgroup\$
    – user
    Dec 24, 2021 at 21:34
3
\$\begingroup\$

Brachylog, 7 bytes

⟦gjz^ᵐ×

Try it online!

Explanation

⟦            Range: [0, …, Input]
 g           Nest in a list: [[0, …, Input]]
  j          Juxtapose: [[0, …, Input], [0, …, Input]]
   z         Zip: [[0, 0], …, [Input, Input]]
    ^ᵐ       Map power: [1, …, Input^Input]
      ×      Multiply: 1 × … × Input^Input
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\$\endgroup\$
3
\$\begingroup\$

K (ngn/k), 6 bytes

*/&!1+

Try it online!

  • !1+ generate 0..x (e.g., with an input of 4, generate 0 1 2 3 4)
  • & take n copies of each n, e.g. zero copies of 0, one copy of 1, two copies of 2, etc.)
  • */ calculate (and implicitly return) the product
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\$\endgroup\$
3
\$\begingroup\$

Thunno 2, 4 bytes

RD*p

Explanation

RD*p  # Implicit input            6
R     # Push the one-range        [1, 2, 3, 4, 5, 6]
  *   # Each to the power of...
 D    # ...itself                 [1, 4, 27, 256, 3125, 46656]
   p  # Product of the list       4031078400000
      # Implicit output
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\$\endgroup\$
3
\$\begingroup\$

BLC, 8 bytes (61 bit)

0000010101110000001011010011100000010111101100111010001100010

Works for Church encoded numerals with 1=i. The code is derived from the common fac function. Degolfed to bruijn:

fac [[1 [[id (1 [[2 1 (1 0)]])]] [1] [0]]]
    id 0

hyperfac [[1 [[exp (1 [[2 1 (1 0)]])]] [1] [0]]]
    exp (0 0)
Improve this answer
\$\endgroup\$
1
  • 1
    \$\begingroup\$ Welcome to Code Golf, and nice answer! \$\endgroup\$
    – Rydwolf Programs
    Oct 14 at 23:05
2
\$\begingroup\$

05AB1E, 4 bytes

LDmP

Try it online or verify all test cases.

Explanation:

L     # Push a list in the range [1, (implicit) input-integer]
      # (note: input 0 will create the list [1,0])
 D    # Duplicate this list
  m   # Take the exponent of the two lists at the same positions
   P  # Take the product of this list
      # (after which the result is output implicitly)
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\$\endgroup\$
2
\$\begingroup\$

MATL, 4 bytes

:t^p

Try it online!

First MATL answer!

Uses the same range-dup-power-product

Improve this answer
\$\endgroup\$
3
  • 1
    \$\begingroup\$ First MATL answer and a very nice one! \$\endgroup\$
    – Luis Mendo
    Oct 4, 2021 at 15:17
  • 1
    \$\begingroup\$ @LuisMendo thank you! MATL is a quite nice golfing language \$\endgroup\$
    – Wasif
    Oct 4, 2021 at 15:59
  • 1
    \$\begingroup\$ It looks like some kind of emoticon, but I can't figure out what's happening with the eyes... \$\endgroup\$
    – DLosc
    Oct 4, 2021 at 22:11
2
\$\begingroup\$

Zsh, 33 bytes

for ((a=1;n++<$1;a*=n**n)):
<<<$a

Attempt This Online!

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\$\endgroup\$
2
\$\begingroup\$

Python 3.8 (pre-release), 59 bytes

from math import*
lambda n:prod(i**i for i in range(1,n+1))

Try it online!

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\$\endgroup\$
2
\$\begingroup\$

Raku, 17 bytes

{[*] [\R*] 1..$_}

Try it online!

  • 1 .. $_ is the sequence of numbers from 1 to the input argument.
  • [\R*] is the "triangular reduction" (scan) of those numbers with the Reversed (and thus right-associative) multiplication operator, producing this list: 𝑛, 𝑛 × (𝑛-1), 𝑛 × (𝑛-1) × (𝑛-2), ..., 𝑛 × (𝑛-1) × (𝑛-2) × ... × 1.
  • [*] is the product of those numbers, which contains 𝑛 factors of 𝑛, 𝑛-1 factors of 𝑛-1, etc, as required.

If the input argument is zero, 1 .. $_ is an empty range, [\R*] applied to that range produces an empty list, and [*] applied to that list returns the multiplicative identity element 1.

Improve this answer
\$\endgroup\$
1
2 3

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