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A193511 a(n) = Sum of even divisors of Omega(n), a(1) = 0.

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%I A193511 #16 Oct 18 2021 17:09:37
%S A193511 0,0,0,2,0,2,0,0,2,2,0,0,0,2,2,6,0,0,0,0,2,2,0,6,2,2,0,0,0,0,0,0,2,2,
%T A193511 2,6,0,2,2,6,0,0,0,0,0,2,0,0,2,0,2,0,0,6,2,6,2,2,0,6,0,2,0,8,2,0,0,0,
%U A193511 2,0,0,0,0,2,0,0,2,0,0,0
%N A193511 a(n) = Sum of even divisors of Omega(n), a(1) = 0.
%C A193511 Omega(n) = number of prime divisors of n counted with multiplicity : A001222 (also called bigomega(n)).
%C A193511 a(1) = 0 by convention.
%H A193511 Antti Karttunen, <a href="/A193511/b193511.txt">Table of n, a(n) for n = 1..10000</a>
%H A193511 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A193511 From _Antti Karttunen_, Jul 23 2017: (Start)
%F A193511 a(1) = 0, for n > 1, a(n) = A146076(A001222(n)).
%F A193511 a(n) + A193512(n) = A290080(n).
%F A193511 (End)
%e A193511 a(16) = 6 because Omega(16) = 4 and the sum of the even divisors of 4 {2, 4} is 6.
%t A193511 Table[Total[Select[Divisors[PrimeOmega[n]], EvenQ[ # ]&]], {n, 58}]
%o A193511 (PARI)
%o A193511 A146076(n) = if(n%2, 0, 2*sigma(n/2)); \\ This function from _Michel Marcus_, Apr 01 2015
%o A193511 A193511(n) = if(1==n,0,A146076(bigomega(n))); \\ _Antti Karttunen_, Jul 23 2017
%Y A193511 Cf. A001222, A146076, A193510, A193512, A290080.
%K A193511 nonn
%O A193511 1,4
%A A193511 _Michel Lagneau_, Jul 29 2011
%E A193511 Description clarified by _Antti Karttunen_, Jul 23 2017