Questions tagged [number-theory]

Number theory involves properties and relationships of numbers, primarily positive integers.

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17
votes
4answers
2k views

Calculate practical numbers

Definition A positive integer n is a practical number (OEIS sequence A005153) iff all smaller positive integers can be represented as sums of distinct divisors of <...
14
votes
12answers
2k views

Print n weird numbers

A weird number is a number that the sum of proper divisors is greater than the number itself and no subset of proper divisors sum to that number. Examples: 70 is a weird number because its proper ...
7
votes
7answers
977 views

Count how many numbers are divisible by perfect numbers in a given range

Given two arbitrary integers \$a\$ and \$b\$, count how many numbers are divisible by perfect numbers in that given range (\$a\$ and \$b\$ both are inclusive). In mathematics, a perfect number is a ...
18
votes
7answers
1k views

Period of the decimal representation

Write a function which takes a single positive integer n and returns the period of the decimal representation of 1/n. Test cases: ...
14
votes
6answers
792 views

Hardy–Ramanujan number generalization

\$1729\$, known as the Hardy–Ramanujan number, is the smallest positive integer that can be expressed as the sum of two cubes of positive integers in two ways (\$12^3+1^3=10^3+9^3=1729\$). Given an ...
6
votes
9answers
4k views

List the first 20 friendly number pairs

I just started reading about friendly numbers and I think they sound great. In number theory, friendly numbers are two or more natural numbers with a common abundancy, the ratio between the sum of ...
4
votes
1answer
312 views

Decompose a range in aligned blocks of size 2^n [closed]

Given an arbitrary contiguous range of positive integers, find the decomposition in the minimum number of sub-ranges of size L = 2^n, with the constraint that each range must be aligned, that is the ...
14
votes
11answers
1k views

N Doors, K Monkeys

There are N doors and K monkeys. Initially, all the doors are closed. Round 1: The 1st monkey visits every door and toggles the door (if the door is closed, it gets opened it; if it is open, it gets ...
7
votes
7answers
1k views

Nth K-Ugly Number

Write the shortest code in any language of your choice to find the \$N\$th \$K\$-ugly number. A \$K\$-ugly number is a number whose only prime factors are the prime numbers \$\le K\$. \$K\$-ugly ...
6
votes
18answers
1k views

Evaluate the primorial of a number [duplicate]

The primorial of a number is the product of all the primes until that number, itself included. Take a number from STDIN as the input and evaluate its primorial, ...
6
votes
3answers
2k views

The making of “Spot It!”: Finding almost unique sets

Puzzle: Find a deck of c cards, each containing p pictures, such that no two pictures match on a given card, and exactly 1 picture on each card matches exactly 1 picture on each of the other cards, ...
21
votes
5answers
2k views

Find largest prime which is still a prime after digit deletion

Over at https://math.stackexchange.com/questions/33094/deleting-any-digit-yields-a-prime-is-there-a-name-for-this the following question is asked. How many primes are there that remain prime after you ...
11
votes
6answers
767 views

Bijection between binary strings and pairs thereof

Input: Either one or two strings consisting of '0's and '1's. If there are 2, they are separated by a space. All strings are of ...
4
votes
2answers
513 views

List ALL prime-factorized natural numbers in ANY order

This is a variant of List prime-factorized natural numbers up to N in ascending order, but the solutions can be very different. Write a program that outputs prime factorizations of all natural ...
8
votes
3answers
1k views

List prime-factorized natural numbers up to N in ascending order

For a given n list prime factorization of all natural numbers between 1 and n in ascending ...
19
votes
19answers
3k views

Calculate hamming weight with low hamming weight

Create a program that computes the hamming weight of a string. Winner is the program with the lowest hamming weight. Rules: Hamming weight for an ASCII character is defined as the total number of ...
16
votes
40answers
2k views

Undulant numbers [duplicate]

An undulant number is a number where its digits alternate between up and down like the following number: 461902 or 708143, or even 1010101, but not 123, because 2 < 3. Write a program or function ...
7
votes
14answers
749 views

Another amicable number problem

Two numbers are said to be 'amicable' or 'friends' if the sum of the proper divisors of the first is equal to the second, and viceversa. For example, the proper divisors of 220 are: 1, 2, 4, 5, 10, ...
17
votes
8answers
902 views

Square Number Digit Density

The square number digit density (SNDD) of a number - invented by myself - is the ratio of the count of square numbers found in consecutive digits to the length of the number. For instance, 169 is a 3-...
24
votes
24answers
3k views

Find the prime factors

In this task, you have to write a program, that computes the prime factors of a number. The input is a natural number 1 < n < 2^32. The output is a list of the prime factors of the number in the ...
8
votes
4answers
865 views

Greatest greatest common divisor

Find the greatest gcd of the numbers \$n^m + k\$ and \$(n+1)^m + k\$ for given m and k. For example, for ...
16
votes
9answers
876 views

Last k digits of Powers of 2

For any integer \$r\$, there exists a power of 2 each of whose last \$r\$ digits are either 1 or 2. Given \$r\$, find the smallest \$x\$ such that \$2^x\bmod{10^r}\$ consists of only 1 or 2. For \$r=...
23
votes
17answers
4k views

Last non-zero digit of n!

Given an integer 1 ≤ N ≤ 1,000,000 as input, output the last non-zero digit of N!, where ! is the factorial (the product of all numbers from 1 to N, inclusive). This is OEIS sequence A008904. Your ...
13
votes
5answers
595 views

Perfect powers in more than one way?

Challenge Your task is to write a program or function which, given a positive integer \$N\$, finds all positive integers less than or equal to \$N\$ that can be expressed as a perfect power in more ...
6
votes
11answers
584 views

Find the largest value of power.

Some numbers can be represented as perfect powers of other numbers. A number x can be represented as x = base^power for some integer base and power. Given an integer x you have to find the largest ...
9
votes
10answers
646 views

Find the number of x-digit numbers whose product of digits is N

Given two numbers \$N\$ and \$x\$, find the number of \$x\$-digit numbers whose product of digits is \$N\$ \$N <10^6\$ and \$x <12\$ ...
18
votes
12answers
806 views

Compute modular inverse

Given two positive numbers \$x\$ and \$n\$ with \$x<2^n\$, write the shortest possible function to compute \$x^{-1} \mod 2^n\$. In other words, find \$y\$ such that \$xy=1 \mod 2^n\$. Your ...
23
votes
6answers
4k views

Hamming numbers

Given a positive integer, print that many hamming numbers, in order. Rules: Input will be a positive integer \$n \le 1,000,000 \$ Output should be the first n terms of https://oeis.org/A051037 ...

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