cp's OEIS Frontend

A218258 a(n) = |{m : multiplicative order of n mod m = 9}|.

%I A218258 #13 Jan 26 2025 02:17:19
%S A218258 0,2,4,26,18,12,52,4,112,12,16,12,30,12,24,488,30,24,64,4,12,78,48,28,
%T A218258 464,12,56,62,72,12,104,56,36,52,48,112,432,28,48,52,48,24,488,56,72,
%U A218258 288,48,24,580,6,24,116,360,44,344,16,48,104,24,8,312,44,112
%N A218258 a(n) = |{m : multiplicative order of n mod m = 9}|.
%H A218258 Alois P. Heinz, <a href="/A218258/b218258.txt">Table of n, a(n) for n = 1..10000</a>
%F A218258 a(n) = tau(n^9-1)-tau(n^3-1), with tau = A000005.
%p A218258 with(numtheory):
%p A218258 a:= n-> add(mobius(9/d) *tau(n^d-1), d={3, 9}):
%p A218258 seq(a(n), n=1..80);
%t A218258 Table[DivisorSigma[0,n^9-1]-DivisorSigma[0,n^3-1],{n,70}] (* _Harvey P. Dale_, Mar 15 2018 *)
%o A218258 (PARI) a(n) = if(n == 1, 0, numdiv(n^9-1) - numdiv(n^3-1)); \\ _Amiram Eldar_, Jan 25 2025
%Y A218258 Row n=9 of A212957.
%Y A218258 Cf. A000005, A008683.
%K A218258 nonn
%O A218258 1,2
%A A218258 _Alois P. Heinz_, Oct 24 2012