A059910 - OEIS

%I #11 Jun 03 2022 03:45:33

%S 0,1,4,6,9,4,4,6,20,9,8,2,6,6,12,44,5,6,18,14,12,4,4,2,56,13,20,4,6,2,

%T 40,6,18,12,12,44,63,6,28,4,16,14,8,2,18,12,28,14,70,3,42,12,42,6,24,

%U 8,56,44,60,6,60,2,4,90,21,20,24,2,18,60,88,6,12,2,28,26,6,28,8,14,170

%N a(n) = |{m : multiplicative order of n mod m = 5}|.

%C The multiplicative order of a mod m, gcd(a,m) = 1, is the smallest natural number d for which a^d = 1 (mod m).

%F a(n) = tau(n^5-1)-tau(n-1), where tau(n) = number of divisors of n A000005. Generally, if b(n, r) = |{m : multiplicative order of n mod m = r}| then b(n, r) = Sum_{d|r} mu(d)*tau(n^(r/d)-1), where mu(n) = Moebius function A008683.

%Y Cf. A059907-A059909, A059911, A059499, A059885-A059892, A002326, A053446-A053452, A002329, A055205, A048691, A048785.

%K easy,nonn

%O 1,3

%A _Vladeta Jovovic_, Feb 08 2001