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.
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.
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.
Smith Number Check
Write a function to check if a number is a Smith number by comparing digit sums of the number and its prime factorization.
Triangular Number
Implement a function that returns the nth triangular number using the closed-form formula.
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 16 challenges · Math & Number Theory
Math & Number Theory — Python coding challenges
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