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A059911 a(n) = |{m : multiplicative order of n mod m = 6}|. 3

%I

%S 0,3,10,16,37,10,42,24,58,53,164,26,68,38,32,68,169,22,222,38,42,50,

%T 328,40,180,219,108,26,334,82,460,82,92,72,220,108,449,86,128,80,192,

%U 22,336,110,222,218,540,84,778,129,150,80,270,54,328,356,132,68,348,22

%N a(n) = |{m : multiplicative order of n mod m = 6}|.

%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^6-1)-tau(n^3-1)-tau(n^2-1)+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.

%e a(2) = |{9,21,63}| = 3, a(3) = |{7,14,28,52,56,91,104,182,364,728}| = 10, a(4) = |{13,35,39,45,65,91,105,117,195,273,315,455,585,819,1365,4095}| = 16,...

%Y Cf. A059907-A059910, A059911-A059916, A059499, A059885-A059892, A002326, A053446-A053453, A055205, A048691, A048785.

%K easy,nonn

%O 1,2

%A _Vladeta Jovovic_, Feb 08 2001

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Last modified March 22 10:07 EDT 2019. Contains 321421 sequences. (Running on oeis4.)