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%I A165825 #22 Feb 17 2022 17:16:49
%S A165825 1,4,4,16,4,16,4,64,16,16,4,64,4,16,16,256,4,64,4,64,16,16,4,256,16,
%T A165825 16,64,64,4,64,4,1024,16,16,16,256,4,16,16,256,4,64,4,64,64,16,4,1024,
%U A165825 16,64
%N A165825 Totally multiplicative sequence with a(p) = 4.
%H A165825 G. C. Greubel, <a href="/A165825/b165825.txt">Table of n, a(n) for n = 1..10000</a>
%F A165825 a(n) = A000302(A001222(n)) = 4^bigomega(n) = 4^A001222(n).
%F A165825 Dirichlet g.f.: Product_{p prime} 1 / (1 - 4 * p^(-s)). - _Ilya Gutkovskiy_, Oct 30 2019
%F A165825 Sum_{k=1..n} a(k) = c * n^2 / (2 * log(2)) + O(n * log(n)^3), where c = Product_{p prime > 2} 1 / (1 - 4/p^2) = 2.6413142332392629671869467536904049315527375203817456105081927074458279809... - _Vaclav Kotesovec_, Feb 17 2022
%t A165825 4^PrimeOmega[Range[100]] (* _G. C. Greubel_, Apr 09 2016 *)
%o A165825 (PARI) a(n) = 4^bigomega(n); \\ _Altug Alkan_, Apr 09 2016
%o A165825 (PARI) for(n=1, 100, print1(direuler(p=2, n, 1/(1 - 4*X))[n], ", ")) \\ _Vaclav Kotesovec_, Feb 17 2022
%Y A165825 Cf. A000302, A001222, A061142, A165824, A351521.
%K A165825 nonn,mult
%O A165825 1,2
%A A165825 _Jaroslav Krizek_, Sep 28 2009

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