A195470 Number of numbers k with 0 <= k < n such that 2^k + 1 is multiple of n.

1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 1, 0, 0, 0, 5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0

Offset: 1

Author

Reinhard Zumkeller, Sep 21 2011

Keywords

• nonn

Comments

a(A014657(n)) > 0; for n > 1: a(A014661(n)) = 0.

Examples

			a(1)=#{0}=1, (2^0 + 1) mod 1;
a(17) = #{4, 12} = 2, (2^4 + 1) mod 17 = (2^12 + 1) mod 17 = 0;
a(18) = #{} = 0;
a(19) = #{9} = 1, (2^9 + 1) mod 19 = 0.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000051, A195610.

Programs

Haskell

a195470 n = length $ filter ((== 0) . (`mod` n)) $
                       take (fromInteger n) a000051_list

Mathematica

nn = 100; pwrs = 2^Range[0, nn] + 1; Table[cnt = 0; Do[If[Mod[pwrs[[i]], n] == 0, cnt++], {i, n}]; cnt, {n, nn}] (* T. D. Noe, Sep 30 2011 *)