A218259 a(n) = |{m : multiplicative order of n mod m = 10}|.

0, 5, 16, 38, 47, 40, 66, 84, 150, 33, 72, 10, 106, 178, 168, 140, 265, 54, 534, 106, 68, 20, 296, 56, 564, 231, 732, 52, 730, 26, 604, 114, 80, 164, 348, 332, 297, 50, 912, 84, 904, 110, 88, 130, 222, 552, 332, 76, 1430, 81, 702, 236, 950, 178, 256, 168, 564

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=10 of A212957.

Cf. A000005, A008683.

Programs

Maple

with(numtheory):
a:= n-> add(mobius(10/d) *tau(n^d-1), d={1, 2, 5, 10}):
seq(a(n), n=1..80);

Mathematica

a[n_] := Total[{1, -1, -1, 1} * DivisorSigma[0, n^{10, 5, 2, 1} - 1]]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jan 25 2025*)

PARI

a(n) = if(n == 1, 0, numdiv(n^10-1) - numdiv(n^5-1) - numdiv(n^2-1) + numdiv(n-1)); \\ Amiram Eldar, Jan 25 2025

Formula

a(n) = tau(n^10-1)-tau(n^5-1)-tau(n^2-1)+tau(n-1), with tau = A000005.