For S(f) = { n : rad(n) divides f(n) }, entire congruence classes of primes divide no element at all: none of S(sigma*_2) is divisible by a prime 3 mod 4, none of S(Phi_3) by a prime 2 mod 3. Also: exactly 1/4 of triples of primes 3 mod 4 are realizable in S(sigma*), against no pair.
number-theory multiplicative-order computational-number-theory arithmetic-functions quadratic-reciprocity unitary-divisors
-
Updated
Sep 6, 2026 - Python