A378161 The number of prime factors of !n = A000166(n), counted with multiplicity.

0, 1, 2, 3, 2, 4, 3, 6, 5, 3, 3, 6, 3, 3, 5, 6, 3, 8, 5, 6, 5, 8, 5, 9, 5, 5, 11, 7, 6, 9, 4, 8, 6, 8, 4, 10, 5, 5, 7, 8, 4, 8, 2, 7, 12, 8, 6, 9, 8, 7, 8, 8, 4, 10, 10, 8, 7, 6, 6, 8, 4, 4, 8, 9, 3, 8, 6, 7, 7, 6, 7, 13, 4, 8, 8, 6, 9, 7, 4, 7, 10, 8, 4, 9, 7

Offset: 2

Author

Amiram Eldar, Nov 18 2024

Keywords

• nonn

Links

• Sean A. Irvine, Table of n, a(n) for n = 2..108

Crossrefs

Cf. A001222, A000166, A152024, A195207, A195208, A195209, A195210, A301423, A378157, A378160, A378162.

Programs

Mathematica

Array[PrimeOmega[Subfactorial[#]] &, 40, 2]

PARI

lista(nmax) = {my(s = 0); for(n = 2, nmax, s = n * s + (-1)^n; print1(bigomega(s), ", "));}

Formula

a(n) = A001222(A000166(n)).

a(n) >= A001222(n-1) + 1 for n >=4, with equality if and only if n is in A301423.

Extensions

a(82)-a(86) from Jinyuan Wang, Nov 24 2024