cp's OEIS Frontend

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

%I A378161 #12 Dec 08 2024 20:41:02
%S A378161 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,
%T A378161 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,
%U A378161 6,7,7,6,7,13,4,8,8,6,9,7,4,7,10,8,4,9,7
%N A378161 The number of prime factors of !n = A000166(n), counted with multiplicity.
%H A378161 Sean A. Irvine, <a href="/A378161/b378161.txt">Table of n, a(n) for n = 2..108</a>
%F A378161 a(n) = A001222(A000166(n)).
%F A378161 a(n) >= A001222(n-1) + 1 for n >=4, with equality if and only if n is in A301423.
%t A378161 Array[PrimeOmega[Subfactorial[#]] &, 40, 2]
%o A378161 (PARI) lista(nmax) = {my(s = 0); for(n = 2, nmax, s = n * s + (-1)^n; print1(bigomega(s), ", "));}
%Y A378161 Cf. A001222, A000166, A152024, A195207, A195208, A195209, A195210, A301423, A378157, A378160, A378162.
%K A378161 nonn
%O A378161 2,3
%A A378161 _Amiram Eldar_, Nov 18 2024
%E A378161 a(82)-a(86) from _Jinyuan Wang_, Nov 24 2024