Nth Triangular Number
Implement a function that returns the nth triangular number efficiently.
Clamp and round to nearest ten
Clamp a number between given bounds and round the result to the nearest ten with halves away from zero.
Integer Square Root Floor
Implement a function that returns the greatest integer whose square is ≤ n, using only integer operations.
Power set size
Compute the size of the power set of a given sequence.
Polynomial evaluator
Implement a polynomial evaluator that computes the value of a polynomial given as a list of coefficients.
Catalan number
Implement a function that returns the nth Catalan number using dynamic programming.
Stirling number
Implement a function to compute Stirling numbers of the second kind S(n,k).
Euler Totient Function
Implement Euler's totient function φ(n) for positive integers.
Prime Factorization
Return a sorted list of prime factors of a positive integer, including repeated factors.
Count divisors
Compute the number of positive divisors of a given integer using its prime factorization.
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.
Abundant Number Check
Implement a function to check whether a given integer is abundant: sum of proper divisors exceeds the number.
Amicable Numbers Check
Write a function that checks if two numbers are an amicable pair by comparing sums of proper divisors.
Happy number check
Implement a function that returns True if a number is happy, False otherwise.
Harshad Number Check
Write a function that checks if a number is a Harshad (or Niven) number.
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.
Lucas Sequence
Implement a function to compute the n-th Lucas number using iteration or recursion with memoization.
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 20 challenges · easy · Math & Number Theory
Math & Number Theory — Python coding challenges
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