Problem 57293. Compute the unitary totient of a number

• Created by ChrisR
• Appears in Cody Problems in Japanese

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The totient function , 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, because 1, 2, 4, 5, 7, and 8 (i.e., six numbers less than 9) are relatively prime to 9.

The unitary totient function 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 ) such that gcd*(k,n) = 1. For example, because the unitary divisors of 9 are 1 and 9. Therefore, for , the largest divisors that are also unitary divisors of 9 are 1-8.

Write a function to compute the unitary totient function.

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Solution Stats

57.14% Correct | 42.86% Incorrect

• 7 Solutions
• 4 Solvers

Last Solution submitted on May 01, 2024

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