A244797 Number of moduli m such that (prime(n) mod m) = 2.

0, 0, 1, 1, 2, 1, 3, 1, 3, 3, 1, 3, 3, 1, 5, 3, 3, 1, 3, 3, 1, 3, 4, 3, 3, 5, 1, 7, 1, 3, 3, 3, 7, 1, 5, 1, 3, 3, 7, 5, 3, 1, 7, 1, 7, 1, 3, 3, 8, 1, 7, 3, 1, 3, 7, 5, 3, 1, 5, 5, 1, 3, 3, 3, 1, 11, 3, 3, 7, 1, 7, 7, 3, 3, 3, 3, 5, 3, 7, 3, 3, 1, 7, 1, 3, 8

Offset: 1

Author

Clark Kimberling, Jul 06 2014

Keywords

• nonn
• easy

Comments

Except for the initial 0,0, this is column 2 of the array at A244740.

Examples

			prime(5) = 11 = (2 mod m) for m = 3, 9 so that a(5) = 2.
		

Links

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

Crossrefs

Cf. A244740, A244796, A244798.

Cf. A032741, A040976.

Programs

Mathematica

z = 300; f[n_, m_] := If[Mod[Prime[n], m] == 2, 1, 0];
t = Table[f[n, m], {n, 1, z}, {m, 1, Prime[n]}];
Table[Count[t[[k]], 1], {k, 1, z}] (* A244797 *)

Formula

a(n) = A032741(A040976(n)). - Ridouane Oudra, Mar 17 2024