A367006 Number of distinct prime factors of n*2^n - 1.

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

Offset: 1

Author

Sean A. Irvine, Oct 31 2023

Keywords

• nonn

Comments

The numbers n*2^n-1 are called Woodall (or Riesel) numbers.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..865

Crossrefs

Cf. A003261, A001221, A366898, A366899.

Programs

Mathematica

Table[PrimeNu[n*2^n - 1], {n, 1, 100}] (* Amiram Eldar, Dec 11 2023 *)

PARI

a(n) = omega(n*2^n - 1); \\ Amiram Eldar, Dec 11 2023

Formula

a(n) = omega(n*2^n - 1) = A001221(A003261(n)).