A367006 -id:A367006 - cp's OEIS frontend

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

Tyler Busby, Oct 26 2023

nonn

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

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

Cf. A001222, A003261, A085723, A366898 (divisors), A367006 (without multiplicity).

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

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

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

A366898 Number of divisors of n*2^n - 1, the Woodall (or Riesel) numbers.

Original entry on oeis.org

1, 2, 2, 6, 4, 2, 4, 4, 4, 4, 6, 4, 12, 10, 8, 48, 8, 4, 8, 4, 16, 16, 8, 8, 4, 8, 8, 16, 24, 2, 8, 4, 8, 32, 8, 32, 4, 8, 4, 24, 16, 8, 32, 8, 16, 24, 40, 16, 16, 8, 8, 16, 24, 8, 16, 8, 16, 6, 32, 8, 8, 16, 8, 512, 48, 16, 12, 48, 16, 8, 8, 4, 24, 16, 2, 256

Offset: 1

Tyler Busby, Oct 26 2023

nonn

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

Cf. A000005, A003261, A002234, A242273, A063515, A056821, A367006, A366899.

Table[DivisorSigma[0, n*2^n - 1], {n, 1, 100}] (* Amiram Eldar, Dec 11 2023 *)

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

a(n) = sigma0(n*2^n - 1) = A000005(A003261(n)).

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

Original entry on oeis.org

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

Sean A. Irvine, Oct 31 2023

nonn

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

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

Cf. A002064, A001221, A367004, A367005, A367006.

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

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

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

cp's OEIS Frontend

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

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A366898 Number of divisors of n*2^n - 1, the Woodall (or Riesel) numbers.

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

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