A218257 a(n) = |{m : multiplicative order of n mod m = 8}|.

0, 4, 14, 8, 28, 8, 48, 72, 88, 36, 56, 48, 112, 48, 100, 16, 108, 72, 228, 16, 112, 96, 128, 12, 176, 72, 304, 32, 112, 48, 448, 144, 224, 64, 84, 48, 456, 144, 64, 48, 528, 48, 2064, 336, 152, 48, 800, 24, 300, 144, 228, 96, 608, 16, 704, 32, 256, 96, 688

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=8 of A212957.

Cf. A000005, A008683.

Programs

Maple

with(numtheory):
a:= n-> add(mobius(8/d) *tau(n^d-1), d={4, 8}):
seq(a(n), n=1..80);

Mathematica

a[n_] := Subtract @@ DivisorSigma[0, {n^8-1, n^4-1}]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jan 25 2025 *)

PARI

a(n) = if(n == 1, 0, numdiv(n^8-1) - numdiv(n^4-1)); \\ Amiram Eldar, Jan 25 2025

Formula

a(n) = tau(n^8-1)-tau(n^4-1), with tau = A000005.