Let \$n=42\$ (Input)
Then divisors are : 1, 2, 3, 6, 7, 14, 21, 42
Squaring each divisor : 1, 4, 9, 36, 49, 196, 441, 1764
Taking sum (adding) : 2500
Since \$50\times 50=2500\$ therefore we return a truthy value. If it is not a perfect square, return a falsy value.
42 ---> true
1 ---> true
246 ---> true
10 ---> false
16 ---> false
This is code-golf so shortest code in bytes for each language wins
Thanks to @Arnauld for pointing out the sequence : A046655
!sum((y=1:(x=scan()))[!x%%y]^2)^.5%%1
Uses the classic "test if perfect square" approach, taking the non-integral part of the square root S^.5%%1 and taking the logical negation of it, as it maps zero (perfect square) to TRUE and nonzero to FALSE.
Thanks to Robert S for saving a couple of bytes!
scan() to save a few bytes?
\$\endgroup\$
Commented
Sep 10, 2018 at 18:31
,.Ajax,.Ford,.Puck,.Act I:.Scene I:.[Enter Ajax and Ford]Ford:Listen tothy.Scene V:.Ajax:You be the sum ofyou a cat.Ford:Is the remainder of the quotient betweenyou I worse a cat?[Exit Ajax][Enter Puck]Ford:If soyou be the sum ofyou the square ofI.[Exit Puck][Enter Ajax]Ford:Be you nicer I?If solet usScene V.[Exit Ford][Enter Puck]Puck:Is the square ofthe square root ofI worse I?You zero.If notyou cat.Open heart
-13 bytes thanks to Jo King!
Outputs 1 for true result, outputs 0 for false result.
Saved 1 byte thanks to @Hedi
n=>!((g=d=>d&&d*d*!(n%d)+g(d-1))(n)**.5%1)
n => // n = input
!( // we will eventually convert the result to a Boolean
(g = d => // g is a recursive function taking the current divisor d
d && // if d is equal to 0, stop recursion
d * d // otherwise, compute d²
* !(n % d) // add it to the result if d is a divisor of n
+ g(d - 1) // add the result of a recursive call with the next divisor
)(n) // initial call to g with d = n
** .5 % 1 // test whether the output of g is a perfect square
) // return true if it is or false otherwise
d going from n to 0 instead of 2 to n like this: n=>!((g=d=>d?d*d*!(n%d)+g(d-1):0)(n)**.5%1)
\$\endgroup\$
𝐅ᛦ𝐬q𝕚
Explanation:
𝐅 Factors
ᛦ Squared
𝐬 Summed
𝕚 is in?
q infinite list of square numbers
f^₂ᵐ+~^₂
-4 bytes thanks to Fatelize cause i didn't realize brachylog has a factors functions
f^₂ᵐ+~^₂ # full code
f # get divisors
^₂ᵐ # square each one
+ # added together
~^₂ # is the result of squaring a number
f^₂ᵐ is 4 bytes shorter than ḋ{⊇×^₂}ᵘ
\$\endgroup\$
─²Σ°
─ Get all divisors as list (implicit input)
² Square (implicit map)
Σ Sum
° Is perfect square?
Very similar to other answers, compared to 05AB1E I gain one byte for my "is perfect square" operator.
Z\UsX^tk=
As simple as it gets
Z\ % Divisors of (implicit) input
U % Square
s % Sum
X^ % Square root
t % Duplicate this value
k= % Is it equal to its rounded value?
param($n)1..$n|%{$a+=$_*$_*!($n%$_)};1..$a|?{$_*$_-eq$a}
Seems long ...
-12 bytes thanks to mazzy
Does exactly what it says on the tin. Takes the range from 1 to input $n and multiplies out the square $_*$_ times whether it's a divisor or not !($n%$_). This makes divisors equal to a nonzero number and non-divisors equal to zero. We then take the sum of them with our accumulator $a. Next, we loop again from 1 up to $a and pull out those numbers where |?{...} it squared is -equal to $a. That is left on the pipeline and output is implicit.
Outputs a positive integer for truthy, and nothing for falsey.
$args[0] is shorter :) 1..$args[0]|%{$a+=$_*$_*!($n%$_)};1..$a|?{$_*$_-eq$a}
\$\endgroup\$
$n inside the loop for !($n%$_). But, your rewrite of the sum saved 12 bytes, so thanks!
\$\endgroup\$
Commented
Sep 10, 2018 at 19:11
$args[0] is shorter :)
\$\endgroup\$
-2 bytes from @Giuseppe and another -2 from @Shaggy
â x²¬v1
â x²¬v1 Full program. Implicity input U
â get all integer divisors of U
x² square each element and sum
¬ square root result
v1 return true if divisible by 1
0=1|.5*⍨2+.*⍨∘∪⍳∨⊢
Anonymous lambda. Returns 1 for truthy and 0 for falsy (test cases in TIO are prettified).
Shoutouts to @H.PWiz for 4 bytes!
0=1|.5*⍨2+.*⍨∘∪⍳∨⊢ ⍝ Main function, argument ⍵ → 42
∨⊢ ⍝ Greatest common divisor (∨) between ⍵ (⊢)
⍳ ⍝ and the range (⍳) [1..⍵]
∪ ⍝ Get the unique items (all the divisors of 42; 1 2 3 6 7 14 21 42)
∘ ⍝ Then
⍨ ⍝ Swap arguments of
2+.* ⍝ dot product (.) of sum (+) and power (*) between the list and 2
⍝ (sums the result of each element in the vector squared)
⍨ ⍝ Use the result vector as base
.5* ⍝ Take the square root
1| ⍝ Modulo 1
0= ⍝ Equals 0
not rather than 0= to save a byte?
\$\endgroup\$
not operator (~), when used monadically, only works with booleans (either 0 or 1). Since any number modulo 1 never equals 1, if I used ~ instead of 0=, I'd get a domain error on any number that's not a perfect square, since decimal values are out of ~'s domain. Furthermore, I cannot simply omit the 0=, since APL's truthy value is 1, not 0, and it wouldn't have a consistent output for falsy values.
\$\endgroup\$
Solution:
{~1!%+/x*x*~1!x%:1+!x}
Explanation:
{~1!%+/x*x*~1!x%:1+!x} / the solution
{ } / lambda taking x as input
!x / range 0..x-1 \
1+ / add 1 |
x%: / x divided by and save result into x |
1! / modulo 1 | get divisors
~ / not |
x* / multiply by x /
x* / multiply by x (aka square) > square
+/ / sum up > sum up
% / square root \
1! / modulo 1 | check if a square
~ / not /
Notes:
@(v)~mod(sqrt(sum(divisors(v).^2)),1)
Unfortunately, it doesn't work on Octave (on tio) so no tio link.
Note As @LuisMendo stated, divisors() belongs to Symbolic Toolbox.
divisors belongs to the Symbolic Toolbox. You should state that in the title. Also, you can use ~··· instead of ···==0
\$\endgroup\$
Commented
Sep 10, 2018 at 21:39
sum(...)^.5 instead of sqrt(sum(...))
\$\endgroup\$
Commented
Dec 11, 2018 at 14:56
-14 bytes thanks to Ørjan Johansen. -11 bytes thanks to ovs.
f x=sum[i^2|i<-[1..x],x`mod`i<1]`elem`map(^2)[1..x^2]
Hey, it's been a while since I've... written any code, so my Haskell and golfing might a bit rusty. I forgot the troublesome Haskell numeric types. :P
ð²ƩĐř²∈
Implicit input
ð Get list of divisors
² Square each element
Ʃ Sum the list [n]
Đ Duplicate the top of the stack
ř² Push the first n square numbers
∈ Is n in the list of square numbers?
Implicit output
ð²Ʃ√ĐƖ=
Implicit input
ð Get list of divisors
² Square each element
Ʃ Sum the list [n]
√ Take the square root of n
Đ Duplicate the top of the stack
Ɩ Cast to an integer
= Are the top two elements on the stack equal to each other?
Implicit output
ð²Ʃ√1%¬
Implicit input
ð Get list of divisors
² Square each element
Ʃ Sum the list [n]
√ Take the square root of n
1% Take the square root of n modulo 1
¬ Negate [python typecasting ftw :)]
Implicit output
Go to Post Office:w 1 l 1 r 1 l.Pickup a passenger going to The Babelfishery.Go to The Babelfishery:s 1 l 1 r.Pickup a passenger going to Cyclone.0 is waiting at Starchild Numerology.0 is waiting at Starchild Numerology.Go to Starchild Numerology:n 1 l 1 l 1 l 2 l.Pickup a passenger going to Rob's Rest.Pickup a passenger going to Addition Alley.Go to Rob's Rest:w 1 r 2 l 1 r.Go to Cyclone:s 1 l 1 l 2 l.[B]Pickup a passenger going to Divide and Conquer.1 is waiting at Starchild Numerology.Go to Starchild Numerology:n 1 r 3 l.Pickup a passenger going to Addition Alley.Go to Addition Alley:w 1 r 3 r 1 r 1 r.Pickup a passenger going to Cyclone.Go to Cyclone:n 1 l 1 l.Pickup a passenger going to Sunny Skies Park.Pickup a passenger going to Divide and Conquer.Go to Divide and Conquer:n 2 r 2 r 1 r.Pickup a passenger going to Cyclone.Go to Sunny Skies Park:e 1 l 1 l 2 l 1 l.Go to Zoom Zoom:n 1 r.Go to Cyclone:w.Pickup a passenger going to Sunny Skies Park.Pickup a passenger going to Equal's Corner.Pickup a passenger going to Trunkers.Go to Sunny Skies Park:n 1 r.Go to Trunkers:s 1 l.Pickup a passenger going to Equal's Corner.Go to Equal's Corner:w 1 l.Switch to plan C if no one is waiting.Pickup a passenger going to Riverview Bridge.Go to Sunny Skies Park:n.Pickup a passenger going to Sunny Skies Park.Pickup a passenger going to Cyclone.Go to Riverview Bridge:n 1 r 1 r.Go to Cyclone:w 2 l.Pickup a passenger going to Cyclone.Go to Sunny Skies Park:n 1 r.Go to Cyclone:n 1 l.Pickup a passenger going to Multiplication Station.Pickup a passenger going to Multiplication Station.Go to Multiplication Station:s 1 l 2 r 4 l.Pickup a passenger going to Addition Alley.Go to Rob's Rest:s 1 r 2 l 1 l 1 r 1 r.Pickup a passenger going to Addition Alley.Go to Addition Alley:s 1 l 1 l 2 r 1 r 1 r.Pickup a passenger going to Rob's Rest.Go to Rob's Rest:n 1 l 1 l 1 l 2 r 1 r.Go to Cyclone:s 1 l 1 l 2 l.Pickup a passenger going to Magic Eight.Go to Sunny Skies Park:n 1 r.Pickup a passenger going to Cyclone.Go to Cyclone:n 1 l.Pickup a passenger going to Cyclone.Pickup a passenger going to Magic Eight.Go to Magic Eight:s 1 l 2 r.Switch to plan D if no one is waiting.Pickup a passenger going to Addition Alley.Go to Cyclone:n 1 l 2 r.Switch to plan B.[C]Go to Sunny Skies Park:n.Pickup a passenger going to Cyclone.Pickup a passenger going to Addition Alley.Go to Cyclone:n 1 l.Switch to plan B.[D]Go to Cyclone:n 1 l 2 r.Pickup a passenger going to Sunny Skies Park.Pickup a passenger going to Sunny Skies Park.Go to Sunny Skies Park:n 1 r.Go to Rob's Rest:s 2 r 1 r.Pickup a passenger going to Cyclone.Go to Cyclone:s 1 l 1 l 2 l.Pickup a passenger going to Cyclone.Pickup a passenger going to Cyclone.Go to Zoom Zoom:n.Go to Cyclone:w.[E]Pickup a passenger going to Joyless Park.Pickup a passenger going to Divide and Conquer.Go to Joyless Park:n 2 r 2 r 2 l.Go to Cyclone:w 1 r 2 l 2 l.Pickup a passenger going to Cyclone.Pickup a passenger going to Joyless Park.Go to Joyless Park:n 2 r 2 r 2 l.Go to Cyclone:w 1 r 2 l 2 l.Pickup a passenger going to Divide and Conquer.Pickup a passenger going to Divide and Conquer.Go to Divide and Conquer:n 2 r 2 r 1 r.Pickup a passenger going to Magic Eight.1 is waiting at Starchild Numerology.Go to Starchild Numerology:e 1 r 3 r 1 l 1 l 2 l.Pickup a passenger going to Magic Eight.Go to Magic Eight:w 1 r 2 r 1 r.Switch to plan F if no one is waiting.Pickup a passenger going to Riverview Bridge.Go to Joyless Park:e 2 l 4 r.Pickup a passenger going to Cyclone.Pickup a passenger going to The Underground.Go to The Underground:w 1 l.Pickup a passenger going to Cyclone.Go to Fueler Up:s.Go to Riverview Bridge:n 3 l.Go to Cyclone:w 2 l.Switch to plan E.[F]Go to Joyless Park:e 2 l 4 r.Pickup a passenger going to What's The Difference.Pickup a passenger going to Cyclone.Go to Cyclone:w 1 r 2 l 2 l.Pickup a passenger going to Multiplication Station.Pickup a passenger going to Multiplication Station.Go to Multiplication Station:s 1 l 2 r 4 l.Pickup a passenger going to What's The Difference.Go to What's The Difference:n 2 l 1 r 3 l.Pickup a passenger going to Knots Landing.Go to Knots Landing:e 4 r 1 l.Pickup a passenger going to The Babelfishery.Go to The Babelfishery:w 1 l.Pickup a passenger going to Post Office.Go to Post Office:n 1 l 1 r.
I went to a lot of places in Townsburg that I've never visited before for this program. Because this program is HUGE (mainly due to the fact that there isn't a one-stop way to take square roots; I still don't actually do that, though), I'm going to attempt to sketch out an explanation of this program.
Go to Post Office:w 1 l 1 r 1 l.
[Take an input line from STDIN.]
Pickup a passenger going to The Babelfishery.
Go to The Babelfishery:s 1 l 1 r.
[Take it to The Babelfishery, which converts the string to a double.]
[If you were to give it a double, it gives back a string.]
Pickup a passenger going to Cyclone.
[We're going to clone this number by sending it to the Cyclone.]
0 is waiting at Starchild Numerology.
[In Taxi, numeric passengers are introduced once they wait at Starchild Numerology.]
[This passenger will be our running squares total.]
0 is waiting at Starchild Numerology.
[This passenger will be our counter, going from 1 to the inputted number.]
[Yes, it's starting at 0 here, but it is incremented at the start of our loop.]
Go to Starchild Numerology:n 1 l 1 l 1 l 2 l.
Pickup a passenger going to Rob's Rest.
Pickup a passenger going to Addition Alley.
Go to Rob's Rest:w 1 r 2 l 1 r.
Go to Cyclone:s 1 l 1 l 2 l.
[Drop off the squares total at Rob's Rest. We'll pick it back up later when we need it.]
[Also, do the actual cloning of the inputted number.]
[At the start of each loop, our only passenger is the counter, going to Addition Alley.]
[B]
Pickup a passenger going to Divide and Conquer.
[Pick up one of the clones of the inputted number.]
[We will leave the other clone here for later.]
1 is waiting at Starchild Numerology.
Go to Starchild Numerology:n 1 r 3 l.
Pickup a passenger going to Addition Alley.
Go to Addition Alley:w 1 r 3 r 1 r 1 r.
Pickup a passenger going to Cyclone.
[Pick up the number 1, and add it to the counter, then pick up the result.]
[This new passenger is our new counter.]
Go to Cyclone:n 1 l 1 l.
Pickup a passenger going to Sunny Skies Park.
Pickup a passenger going to Divide and Conquer.
[First we pick up the other clone of the inputted number, going to Sunny Skies Park.]
[Sunny Skies Park is basically a First-In-First-Out queue, where we will stick it for later.]
[Then we pick up a clone of the counter which we just dropped off, so we can divide the input by it.]
[We will leave the other clone here for later.]
Go to Divide and Conquer:n 2 r 2 r 1 r.
Pickup a passenger going to Cyclone.
[Divide the inputted number by the counter, and prepare to clone it.]
Go to Sunny Skies Park:e 1 l 1 l 2 l 1 l.
[Drop off our clone of the inputted number at Sunny Skies Park.]
Go to Zoom Zoom:n 1 r.
[Can't forget to get gas!]
[Zoom Zoom is a close gas station, and we have so many credits that one stop here every iteration fills us up completely.]
Go to Cyclone:w.
Pickup a passenger going to Sunny Skies Park.
Pickup a passenger going to Equal's Corner.
Pickup a passenger going to Trunkers.
[First we pick up the other clone of the counter, going to Sunny Skies Park for later.]
[Then we pick up a clone of the division result, going to Equal's Corner.]
[Equal's Corner takes multiple numeric passengers, and returns the value of one of them if they are equal, but otherwise it returns no one.]
[Finally we pick up the other clone of the division result, going to Trunkers.]
[Dropping off a passenger at Trunkers is equivalent to the floor function. We need it here because division results are "exact".]
[(Well, as exact as double precision arithmetic can be.)]
[We will compare the result of this to the exact result of the division.]
Go to Sunny Skies Park:n 1 r.
[Drop off our clone of the counter at Sunny Skies Park.]
Go to Trunkers:s 1 l.
Pickup a passenger going to Equal's Corner.
Go to Equal's Corner:w 1 l.
[Compare the exact division result with the floored division result.]
[If they are equal, then the value of one of them will be waiting.]
[This also means that the counter is a divisor of the input, and we should add the square of the counter to our running squares total.]
[If they are not equal, no one will be waiting, the counter is not a divisor of the input, and nothing should happen.]
Switch to plan C if no one is waiting.
[This is Taxi's only conditional operator.]
[It jumps to a bracketed label (in this case, C) if there is no one waiting at this stop.]
[Of course, there is an unconditional version of this, too.]
[If we are on this path, we are adding the square of the counter to our running squares total.]
Pickup a passenger going to Riverview Bridge.
[We don't actually need the passenger that's waiting here (and leaving it there will not work at all).]
[So what do you do when you have a pesky passenger you don't want? You take them to Riverview Bridge!]
[Riverview Bridge has a lovely view, but passengers dropped off there always seem to fall in the river.]
[This means you don't collect your fare for bringing them there, but at least the pesky passenger is gone.]
Go to Sunny Skies Park:n.
Pickup a passenger going to Sunny Skies Park.
Pickup a passenger going to Cyclone.
[We want to pick up the counter (so we can multiply it by itself). That dang input is in the way, but we still need it.]
[So what do we do? We just take it back to where it was waiting!]
[Yup, even though one would never do this in real life, a passenger's current location is a perfectly legal destination in Taxi.]
Go to Riverview Bridge:n 1 r 1 r.
[So long, Equal's Corner result!]
Go to Cyclone:w 2 l.
Pickup a passenger going to Cyclone.
Go to Sunny Skies Park:n 1 r.
[We clone the counter so we can still use it, then we drop the inputted number back at Sunny Side Park.]
[Again, we will leave the other clone here for later.]
Go to Cyclone:n 1 l.
Pickup a passenger going to Multiplication Station.
Pickup a passenger going to Multiplication Station.
Go to Multiplication Station:s 1 l 2 r 4 l.
[Square the counter.]
Pickup a passenger going to Addition Alley.
Go to Rob's Rest:s 1 r 2 l 1 l 1 r 1 r.
Pickup a passenger going to Addition Alley.
Go to Addition Alley:s 1 l 1 l 2 r 1 r 1 r.
Pickup a passenger going to Rob's Rest.
Go to Rob's Rest:n 1 l 1 l 1 l 2 r 1 r.
[Pick up the running squares total from Rob's Rest, add it to the square of the counter, then bring it back.]
Go to Cyclone:s 1 l 1 l 2 l.
Pickup a passenger going to Magic Eight.
[Pick up the counter, going to Magic Eight.]
[Magic Eight takes two numeric passengers, and returns the first passenger if it is less than the second, but otherwise it returns no one.]
[We will compare the counter to the inputted number...]
Go to Sunny Skies Park:n 1 r.
Pickup a passenger going to Cyclone.
Go to Cyclone:n 1 l.
Pickup a passenger going to Cyclone.
Pickup a passenger going to Magic Eight.
[...who we take now, so we can make a clone of it and compare it to the counter.]
Go to Magic Eight:s 1 l 2 r.
Switch to plan D if no one is waiting.
[Compare.]
[If the counter is waiting here, the loop is to continue.]
[If not, switch to plan D, end the loop, and start detecting whether or not the running squares total is a square itself.]
Pickup a passenger going to Addition Alley.
Go to Cyclone:n 1 l 2 r.
Switch to plan B.
[Reset everything, and loop back to the start of plan B.]
[C]
[If we are on this path, the counter is not a divisor of the inputted number, but the loop should continue anyways.]
Go to Sunny Skies Park:n.
Pickup a passenger going to Cyclone.
Pickup a passenger going to Addition Alley.
Go to Cyclone:n 1 l.
Switch to plan B.
[Reset everything, and loop back to the start of plan B.]
[D]
[We are finally out of the loop. Now it's time for the real fun.]
Go to Cyclone:n 1 l 2 r.
Pickup a passenger going to Sunny Skies Park.
Pickup a passenger going to Sunny Skies Park.
Go to Sunny Skies Park:n 1 r.
[We don't need the inputted number anymore, but we can't change its destination from the Cyclone.]
[So we go to the Cyclone, so we can take the two clones and bring them to Sunny Skies Park forever.]
[We could send them to Riverview Bridge, but that will take more bytes.]
Go to Rob's Rest:s 2 r 1 r.
[Pick up our running squares total from Rob's Rest, so it can go out and see the town.]
Pickup a passenger going to Cyclone.
Go to Cyclone:s 1 l 1 l 2 l.
Pickup a passenger going to Cyclone.
Pickup a passenger going to Cyclone.
Go to Zoom Zoom:n.
Go to Cyclone:w.
[We need to end up with 4 clones of the total.]
[Two of them will actually be used as the counter in this loop.]
[At the start of each loop, we have no passengers.]
[E]
Pickup a passenger going to Joyless Park.
Pickup a passenger going to Divide and Conquer.
Go to Joyless Park:n 2 r 2 r 2 l.
[We will leave one clone of the total at Joyless Park (like Sunny Side Park, but on the opposite side of town).]
[The other clone will be used in a division.]
Go to Cyclone:w 1 r 2 l 2 l.
Pickup a passenger going to Cyclone.
Pickup a passenger going to Joyless Park.
Go to Joyless Park:n 2 r 2 r 2 l.
[We will leave one clone of the counter at Joyless Park.]
[We will clone the other clone (clone-ception?).]
Go to Cyclone:w 1 r 2 l 2 l.
Pickup a passenger going to Divide and Conquer.
Pickup a passenger going to Divide and Conquer.
Go to Divide and Conquer:n 2 r 2 r 1 r.
[We will use both clones of the counter in a division.]
[Divide and Conquer can take 3 arguments, and the result here will be equivalent to total / counter^2 .]
[If the square of the counter is equal to the total, the result will be 1.]
[If the square of the counter is less than the total, the result will be greater than 1.]
[If the square of the counter is greater than the total, the result will be less than 1.]
Pickup a passenger going to Magic Eight.
1 is waiting at Starchild Numerology.
Go to Starchild Numerology:e 1 r 3 r 1 l 1 l 2 l.
Pickup a passenger going to Magic Eight.
Go to Magic Eight:w 1 r 2 r 1 r.
Switch to plan F if no one is waiting.
[We compare the result of the division against 1 to decide our next course of action.]
[If it is greater or equal, the loop should end, and the counter is equal to the floor of the square root.]
[If it is less, the loop should continue.]
Pickup a passenger going to Riverview Bridge.
[Whoops, we don't actually need this anymore.]
Go to Joyless Park:e 2 l 4 r.
Pickup a passenger going to Cyclone.
[We will clone the total later, so we can reuse it in the next loop iteration.]
Pickup a passenger going to The Underground.
Go to The Underground:w 1 l.
[Instead of taking the number 1 and subtracting it from the counter, we can do an optimization here.]
[The Underground is a destination that takes 1 passenger, and subtracts 1 from it.]
[If the result is positive, it returns the result. Otherwise, it returns no one.]
[The latter result will not happen for us, however.]
Pickup a passenger going to Cyclone.
[We will clone the counter later, so we can reuse it in the next loop iteration.]
Go to Fueler Up:s.
[Gotta remember to stop for gas!]
Go to Riverview Bridge:n 3 l.
[So long, Magic Eight result!]
Go to Cyclone:w 2 l.
Switch to plan E.
[Reset everything, and loop back to the start of plan E.]
[F]
Go to Joyless Park:e 2 l 4 r.
Pickup a passenger going to What's The Difference.
Pickup a passenger going to Cyclone.
[Once we've figured out the square root of the total, we're still not done.]
Go to Cyclone:w 1 r 2 l 2 l.
Pickup a passenger going to Multiplication Station.
Pickup a passenger going to Multiplication Station.
Go to Multiplication Station:s 1 l 2 r 4 l.
[We actually square the square root...]
Pickup a passenger going to What's The Difference.
Go to What's The Difference:n 2 l 1 r 3 l.
[...and subtract it from the total at What's The Difference (which subtracts dropped-off passengers).]
Pickup a passenger going to Knots Landing.
Go to Knots Landing:e 4 r 1 l.
[If the result is 0, the total is a perfect square, and a truthy value should be output.]
[If the result is nonzero, the total is not a perfect square, and a falsy value should be output.]
[Luckily, Knots Landing does our work for us.]
[Knots Landing inverts the boolean logic of numeric passengers (i.e. 0 becomes 1, nonzero becomes 0).]
Pickup a passenger going to The Babelfishery.
Go to The Babelfishery:w 1 l.
[Convert it to a string...]
Pickup a passenger going to Post Office.
Go to Post Office:n 1 l 1 r.
[...and output it.]
[We would exit the program by going to the Taxi Garage, but that takes bytes.]
[The boss fires us because we didn't bring the taxi back to the garage, but that gets output to STDERR, so that's OK.]
K²∑∆²
∆² # Is
∑ # The sum of
² # The squares of
K # The factors of the input
∆² # A perfect square?
£İ□ṁ□Ḋ
£İ□ṁ□Ḋ -- example input 12
Ḋ -- divisors: [1,2,3,4,6,12]
ṁ -- map the following ..
□ -- | square: [1,4,9,16,36,144]
-- .. and sum: 210
£ -- is it element of (assumes sorted)
İ□ -- | list of squares: [1,4,9,16..196,225,..
ÆD²SƲ
Try it online! Or see the test-suite.
ÆD²SƲ - Main Link: integer
ÆD - divisors
² - square
S - sum
Ʋ - is square?
IntegerQ@Sqrt[2~DivisorSigma~#]&
Pure function. Takes a number as input and returns True or False as output. Not entirely sure if there's a shorter method for checking perfect squares.
def j(s:Int)=Math.sqrt((1 to s).filter(s%_<1).map(a=>a*a).sum)%1==0
