A367008 Number of prime factors of n*2^n + 1, counted with multiplicity.

0, 1, 2, 2, 2, 2, 3, 3, 2, 2, 4, 2, 3, 3, 3, 3, 2, 4, 4, 4, 5, 2, 4, 4, 4, 4, 5, 4, 3, 3, 6, 6, 3, 2, 5, 2, 4, 3, 4, 3, 3, 4, 4, 5, 4, 4, 5, 5, 4, 5, 6, 3, 6, 3, 5, 4, 4, 5, 5, 4, 4, 7, 3, 3, 7, 5, 9, 5, 4, 5, 5, 6, 5, 5, 5, 5, 5, 4, 4, 6, 4, 4, 4, 5, 4, 7, 6

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, A001222, A366899, A367007.

Programs

Mathematica

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

PARI

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

Formula

a(n) = bigomega(n*2^n + 1) = A001222(A002064(n)).