[seqfan] Generalization of the totient

Charles Greathouse charles.greathouse at case.edu
Wed Jan 24 08:36:44 CET 2018

I'm interested in the function f(m, n) which counts the number of k, 1 <= k
<= n, such that m and k are squarefree. This function generalizes Euler's
totient: f(n, n) = phi(n). Can this be computed efficiently in the more
general case where m and n are unequal? (You can assume the factorization
of m is known and m and n are of the same order of magnitude.) Is anything
interesting known about this function?

Charles Greathouse
Case Western Reserve University

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