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

1,17

Comments

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000051, A195610.

Sequence in context: A219484 A060396 A353353 * A324902 A252370 A045827

Adjacent sequences: A195467 A195468 A195469 * A195471 A195472 A195473

Keyword

nonn

Author

Reinhard Zumkeller, Sep 21 2011

Status

approved