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

%I A378160 #13 Dec 08 2024 20:41:07
%S A378160 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,
%T A378160 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,
%U A378160 6,6,7,7,4,8,6,5,8,6,4,4,5,8,4,7,7,8,6
%N A378160 The number of distinct prime factors of !n = A000166(n).
%H A378160 Sean A. Irvine, <a href="/A378160/b378160.txt">Table of n, a(n) for n = 2..108</a>
%F A378160 a(n) = A001221(A000166(n)).
%F A378160 a(n) >= A001221(n-1) + 1 for n >=5.
%t A378160 Array[PrimeNu[Subfactorial[#]] &, 40, 2]
%o A378160 (PARI) lista(nmax) = {my(s = 0); for(n = 2, nmax, s = n * s + (-1)^n; print1(omega(s), ", "));}
%Y A378160 Cf. A000166, A001221, A152024, A195207, A195208, A195209, A195210, A301423, A378157, A378161, A378162.
%K A378160 nonn
%O A378160 2,4
%A A378160 _Amiram Eldar_, Nov 18 2024
%E A378160 a(82)-a(88) from _Jinyuan Wang_, Nov 24 2024