A367007 Number of distinct prime factors of n*2^n + 1.

0, 1, 1, 1, 2, 2, 3, 3, 2, 2, 3, 2, 3, 2, 3, 3, 2, 3, 4, 4, 3, 2, 4, 4, 4, 4, 4, 4, 2, 3, 5, 5, 3, 2, 5, 2, 3, 3, 3, 3, 3, 4, 4, 5, 4, 4, 5, 5, 4, 2, 6, 3, 6, 3, 5, 4, 3, 5, 5, 4, 4, 7, 3, 3, 6, 5, 7, 4, 4, 5, 5, 5, 5, 5, 3, 5, 4, 4, 4, 6, 4, 4, 4, 5, 4, 6, 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, A001221, A367004, A367005, A367006.

Programs

Mathematica

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

PARI

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

Formula

a(n) = omega(n*2^n + 1) = A001221(A002064(n)).