A067718 Numbers k such that sigma(2^k+1) == 0 (mod k).

1, 2, 6, 12, 24, 36, 42, 70, 126, 132, 144, 168, 210, 225, 252, 336, 344, 378, 385, 396, 462, 504, 528, 546, 560, 561, 576, 627, 630, 660, 672, 693, 714, 798, 896, 924, 930, 945, 960, 1001, 1008, 1012, 1032, 1050, 1116

Offset: 1

Author

Benoit Cloitre, Feb 05 2002

Keywords

• nonn
• hard
• more

Comments

1155 is also a term. - Husnain Raza, Oct 23 2024

Links

• Husnain Raza, Github link

Crossrefs

Cf. A000051, A000203, A069061.

Programs

Mathematica

Select[Range[150], Divisible[DivisorSigma[1, 2^# + 1], #] &] (* Amiram Eldar, Nov 28 2020 *)

PARI

isok(n)=sigma(2^n+1)%n==0 \\ Klaus Brockhaus, Apr 13 2005

Extensions

a(13)-a(15) from Klaus Brockhaus, Apr 13 2005

a(16)-a(21) from Lars Blomberg, Jul 28 2017

a(22)-a(44) from Amiram Eldar, Nov 28 2020

a(45) from Husnain Raza, Sep 18 2024