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A059908 a(n) = |{m : multiplicative order of n mod m = 3}|. 4

%I

%S 0,1,2,4,3,2,8,2,12,5,12,2,12,2,4,20,5,6,10,2,6,14,12,2,40,9,4,6,18,

%T 10,16,6,6,8,12,12,39,2,12,8,8,6,16,6,18,26,12,6,50,3,18,8,18,2,32,12,

%U 8,20,4,6,60,2,12,26,21,4,64,10,6,8,8,6,20,14,4,12,6,4,64,2,70,7,12,6,24

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

%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).

%H Alois P. Heinz, <a href="/A059908/b059908.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = tau(n^3-1)-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) = |{7}| = 1, a(3) = |{13,26}| = 2, a(4) = |{7,9,21,63}| = 4, a(5) = |{31,62,124}| = 3, a(6) = |{43,215}| = 2, a(7) = |{9,18,19,38,57,114,171,342}| = 8,...

%t Table[DivisorSigma[0,n^3-1]-DivisorSigma[0,n-1],{n,90}] (* _Harvey P. Dale_, Feb 03 2015 *)

%Y Cf. A059907, A059909-A059916, A059499, A059885-A059892, A002326, A053446-A053453, A055205, A048691, A048785.

%Y Row n=3 of A212957. - _Alois P. Heinz_, Oct 24 2012

%K easy,nonn

%O 1,3

%A _Vladeta Jovovic_, Feb 08 2001

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Last modified February 19 07:51 EST 2019. Contains 320309 sequences. (Running on oeis4.)