|
%I #7 Jan 05 2024 10:13:16
%S 0,1,1,2,1,2,1,2,2,1,3,1,2,2,1,3,1,3,2,2,1,2,2,3,1,3,1,2,2,2,4,1,2,2,
%T 1,3,1,3,3,2,1,2,3,2,3,1,2,2,2,1,4,1,2,3,2,3,1,3,2,3,1,1,2,3,3,2,3,1,
%U 2,1,4,2,2,2,1,4,2,3,2,2,2,1,3,3,4,1,3
%N The number of prime factors of the cubefree numbers, counted with multiplicity.
%H Amiram Eldar, <a href="/A368779/b368779.txt">Table of n, a(n) for n = 1..10000</a>
%H Rafael Jakimczuk and Matilde Lalín, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL25/Lalin/lalin2.html">The Number of Prime Factors on Average in Certain Integer Sequences</a>, Journal of Integer Sequences, Vol. 25 (2022), Article 22.2.3.
%F a(n) = A001222(A004709(n)).
%F Sum_{a(n) <= x} = (1/zeta(3)) * x * log(log(x)) + O(x) (Jakimczuk and Lalín, 2022).
%t f[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, If[AllTrue[e, # < 3 &], Total[e], Nothing]]; f[1] = 0; Array[f, 100]
%o (PARI) lista(max) = {my(e); for(k = 1, max, e = factor(k)[,2]; if(k == 1 || vecmax(e) < 3, print1(vecsum(e), ", ")));}
%Y Cf. A001222, A004709, A072047.
%K nonn,easy
%O 1,4
%A _Amiram Eldar_, Jan 05 2024
|
