A366899 Number of prime factors of n*2^n - 1, counted with multiplicity.

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

Offset: 1

Author

Tyler Busby, Oct 26 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. A001222, A003261, A085723, A366898 (divisors), A367006 (without multiplicity).

Programs

Mathematica

Table[PrimeOmega[n*2^n - 1], {n, 1, 100}] (* Amiram Eldar, Dec 09 2023 *)

PARI

a(n) = bigomega(n*2^n - 1); \\ Michel Marcus, Dec 09 2023

Formula

a(n) = bigomega(n*2^n - 1) = A001222(A003261(n)).