Nth Triangular Number
Implement a function that returns the nth triangular number efficiently.
Integer Square Root Floor
Implement a function that returns the greatest integer whose square is ≤ n, using only integer operations.
Catalan number
Implement a function that returns the nth Catalan number using dynamic programming.
Sieve of Eratosthenes
Implement the Sieve of Eratosthenes to return a sorted list of all primes up to a given integer n.
Prime Factorization
Return a sorted list of prime factors of a positive integer, including repeated factors.
Sum of divisors
Given an integer n, return the sum of all its positive divisors.
Perfect Number Check
Write a function that returns True if a number is perfect, i.e., equal to the sum of its proper divisors.
Happy number check
Implement a function that returns True if a number is happy, False otherwise.
Triangular Number
Implement a function that returns the nth triangular number using the closed-form formula.
Pentagonal Number
Given a positive integer n, return the nth pentagonal number using the formula P(n) = n(3n - 1)/2.
Partition function
Write a function that returns the number of ways to write a positive integer as a sum of positive integers (order irrelevant).
Showing 11 challenges · Math & Number Theory
Math & Number Theory — Python coding challenges
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