A165825 - OEIS

%I #22 Feb 17 2022 17:16:49

%S 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 16,64,64,4,64,4,1024,16,16,16,256,4,16,16,256,4,64,4,64,64,16,4,1024,

%U 16,64

%N Totally multiplicative sequence with a(p) = 4.

%H G. C. Greubel, <a href="/A165825/b165825.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000302(A001222(n)) = 4^bigomega(n) = 4^A001222(n).

%F Dirichlet g.f.: Product_{p prime} 1 / (1 - 4 * p^(-s)). - _Ilya Gutkovskiy_, Oct 30 2019

%F 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 4^PrimeOmega[Range[100]] (* _G. C. Greubel_, Apr 09 2016 *)

%o (PARI) a(n) = 4^bigomega(n); \\ _Altug Alkan_, Apr 09 2016

%o (PARI) for(n=1, 100, print1(direuler(p=2, n, 1/(1 - 4*X))[n], ", ")) \\ _Vaclav Kotesovec_, Feb 17 2022

%Y Cf. A000302, A001222, A061142, A165824, A351521.

%K nonn,mult

%O 1,2

%A _Jaroslav Krizek_, Sep 28 2009