A165781 a(n) = (2^A002326(n)-1)/(2*n+1).

1, 1, 3, 1, 7, 93, 315, 1, 15, 13797, 3, 89, 41943, 9709, 9256395, 1, 31, 117, 1857283155, 105, 25575, 381, 91, 178481, 42799, 5, 84973577874915, 19065, 4599, 4885260612740877, 18900352534538475, 1, 63, 1101298153654301589

Offset: 0

Author

Ctibor O. Zizka, Sep 26 2009

Keywords

• easy
• nonn

Comments

a(n) = 1 <=> n is in A000225 <=> n = 2^k - 1 with k = 0, 1, 2, ... - M. F. Hasler, Sep 20 2017

Links

• Robert Israel, Table of n, a(n) for n = 0..1672

Crossrefs

Cf. A002326, A053446, A000225.

Programs

Maple

A002326 := proc(n) if n = 0 then 1 ; else numtheory[order](2,2*n+1) ; end if ; end proc:
A165781 := proc(n) (2^A002326(n)-1)/(2*n+1) ; end proc:
seq(A165781(n),n=0..60) ; # R. J. Mathar, Nov 16 2009

Mathematica

a[n_] := (2^MultiplicativeOrder[2, 2n+1]-1)/(2n+1);
a /@ Range[0, 40] (* Jean-François Alcover, Jun 04 2020 *)

PARI

a(n)=(2^znorder(Mod(2,n=2*n+1))-1)/n \\ M. F. Hasler, Sep 20 2017

Extensions

Sign in definition and offset corrected by R. J. Mathar, Nov 16 2009