A367009 Number of divisors of n*2^n + 1.

1, 2, 3, 3, 4, 4, 8, 8, 4, 4, 12, 4, 8, 6, 8, 8, 4, 12, 16, 16, 16, 4, 16, 16, 16, 16, 24, 16, 6, 8, 48, 48, 8, 4, 32, 4, 12, 8, 12, 8, 8, 16, 16, 32, 16, 16, 32, 32, 16, 10, 64, 8, 64, 8, 32, 16, 12, 32, 32, 16, 16, 128, 8, 8, 96, 32, 256, 24, 16, 32, 32, 48

Offset: 0

Author

Sean A. Irvine, Oct 31 2023

Keywords

• nonn

Comments

The numbers n*2^n+1 are called Cullen numbers.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..865

Crossrefs

Cf. A002064, A000005, A366898, A367007, A367008.

Programs

Mathematica

Table[DivisorSigma[0, n*2^n + 1], {n, 0, 100}] (* Amiram Eldar, Jan 06 2024 *)

PARI

a(n) = numdiv(n*2^n + 1); \\ Amiram Eldar, Jan 06 2024

Formula

a(n) = sigma0(n*2^n + 1) = A000005(A002064(n)).