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

0, 2, 4, 26, 18, 12, 52, 4, 112, 12, 16, 12, 30, 12, 24, 488, 30, 24, 64, 4, 12, 78, 48, 28, 464, 12, 56, 62, 72, 12, 104, 56, 36, 52, 48, 112, 432, 28, 48, 52, 48, 24, 488, 56, 72, 288, 48, 24, 580, 6, 24, 116, 360, 44, 344, 16, 48, 104, 24, 8, 312, 44, 112

Offset: 1

Author

Alois P. Heinz, Oct 24 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Row n=9 of A212957.

Cf. A000005, A008683.

Programs

Maple

with(numtheory):
a:= n-> add(mobius(9/d) *tau(n^d-1), d={3, 9}):
seq(a(n), n=1..80);

Mathematica

Table[DivisorSigma[0,n^9-1]-DivisorSigma[0,n^3-1],{n,70}] (* Harvey P. Dale, Mar 15 2018 *)

PARI

a(n) = if(n == 1, 0, numdiv(n^9-1) - numdiv(n^3-1)); \\ Amiram Eldar, Jan 25 2025

Formula

a(n) = tau(n^9-1)-tau(n^3-1), with tau = A000005.