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

2,3

Links

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

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A351955 A174523 A363159 * A261172 A374192 A134834

Adjacent sequences: A378158 A378159 A378160 * A378162 A378163 A378164

Keyword

nonn

Author

Amiram Eldar, Nov 18 2024

Extensions

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

Status

approved