A244796 Number of moduli m such that (prime(n) mod m) = 1.

0, 1, 2, 3, 3, 5, 4, 5, 3, 5, 7, 8, 7, 7, 3, 5, 3, 11, 7, 7, 11, 7, 3, 7, 11, 8, 7, 3, 11, 9, 11, 7, 7, 7, 5, 11, 11, 9, 3, 5, 3, 17, 7, 13, 8, 11, 15, 7, 3, 11, 7, 7, 19, 7, 8, 3, 5, 15, 11, 15, 7, 5, 11, 7, 15, 5, 15, 19, 3, 11, 11, 3, 7, 11, 15, 3, 5, 17

Offset: 1

Author

Clark Kimberling, Jul 06 2014

Keywords

• nonn
• easy

Comments

Except for the initial 0, this is column 1 of the array at A244740,

Examples

			prime(5) = 11 = (1 mod m) for m = 2, 5, 10, so that a(5) = 3.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A244740, A244797, A244798.

Programs

Mathematica

z = 300; f[n_, m_] := If[Mod[Prime[n], m] == 1, 1, 0];
t = Table[f[n, m], {n, 1, z}, {m, 1, Prime[n]}];
Table[Count[t[[k]], 1], {k, 1, z}] (* A244796 *)

Formula

a(n) = A000005(prime(n) - 1) - 1. - Gionata Neri, Jul 04 2017