A218256 a(n) = |{m : multiplicative order of n mod m = 7}|.

0, 1, 2, 6, 3, 2, 12, 10, 12, 9, 12, 6, 6, 2, 8, 60, 5, 6, 18, 14, 42, 8, 12, 14, 56, 3, 12, 12, 12, 14, 8, 14, 18, 12, 12, 44, 27, 2, 12, 4, 24, 6, 40, 14, 42, 6, 12, 6, 150, 5, 18, 60, 18, 14, 24, 4, 40, 12, 60, 2, 12, 6, 12, 138, 49, 4, 24, 2, 18, 12, 40, 2

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=7 of A212957.

Cf. A000005, A008683.

Programs

Maple

with(numtheory):
a:= n-> add(mobius(7/d) *tau(n^d-1), d={1, 7}):
seq(a(n), n=1..80);

Mathematica

a[n_] := Subtract @@ DivisorSigma[0, {n^7-1, n-1}]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jan 25 2025 *)

PARI

a(n) = if(n == 1, 0, numdiv(n^7-1) - numdiv(n-1)); \\ Amiram Eldar, Jan 25 2025

Formula

a(n) = tau(n^7-1)-tau(n-1), with tau = A000005.