A378160 The number of distinct prime factors of !n = A000166(n).

0, 1, 1, 2, 2, 3, 3, 4, 2, 3, 2, 4, 3, 3, 4, 3, 3, 4, 5, 5, 4, 7, 5, 6, 4, 5, 7, 6, 6, 7, 4, 4, 4, 8, 4, 6, 4, 5, 6, 6, 4, 7, 2, 4, 7, 8, 6, 5, 7, 6, 7, 7, 4, 6, 9, 6, 6, 6, 6, 6, 4, 4, 5, 4, 3, 6, 6, 6, 6, 6, 7, 7, 4, 8, 6, 5, 8, 6, 4, 4, 5, 8, 4, 7, 7, 8, 6

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. A000166, A001221, A152024, A195207, A195208, A195209, A195210, A301423, A378157, A378161, A378162.

Programs

Mathematica

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

PARI

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

Formula

a(n) = A001221(A000166(n)).

a(n) >= A001221(n-1) + 1 for n >=5.

Extensions

a(82)-a(88) from Jinyuan Wang, Nov 24 2024