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.
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.
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.
Armstrong Number Check
Implement a function that checks if a given integer is an Armstrong number.
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).
Multiply without multiply
Write a function that multiplies two integers using only addition, subtraction, and bit shifts — no * operator.
Showing 23 challenges · easy · Math & Number Theory
Math & Number Theory — Python coding challenges
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