Problem 57293. Compute the unitary totient of a number

The totient function phi(n), the subject of Cody Problems 656 and 50182, gives the number of integers smaller than n that are relatively prime to n--that is, that share no common factors with n other than 1. Therefore, phi(9) = 6 because 1, 2, 4, 5, 7, and 8 (i.e., six numbers less than 9) are relatively prime to 9.
The unitary totient function phi*(n) is defined in terms of the function gcd*(k,n), which is the largest divisor of k that is also a unitary divisor of n. Then the unitary totient function gives the number of k (with 1 <= k <= n) such that gcd*(k,n) = 1. For example, phi*(9) = 8 because the unitary divisors of 9 are 1 and 9. Therefore, for 1, 2, 3,...,8, the largest divisors that are also unitary divisors of 9 are 1-8.
Write a function to compute the unitary totient function.
Solve

Solution Stats

57.14% Correct | 42.86% Incorrect
Last Solution submitted on May 01, 2024

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers4

Suggested Problems

More from this Author281

Problem Tags

number theory sequence

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!