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A193512 a(n) = Sum of odd divisors of Omega(n), a(1) = 0.

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%I A193512 #17 Jul 23 2017 21:48:27
%S A193512 0,1,1,1,1,1,1,4,1,1,1,4,1,1,1,1,1,4,1,4,1,1,1,1,1,1,4,4,1,4,1,6,1,1,
%T A193512 1,1,1,1,1,1,1,4,1,4,4,1,1,6,1,4,1,4,1,1,1,1,1,1,1,1,1,1,4,4,1,4,1,4,
%U A193512 1,4,1,6,1,1,4,4,1,4,1,6,1,1,1,1,1,1,1,1,1,1,1,4,1,1,1,4,1,4,4,1,1,4,1,1,4
%N A193512 a(n) = Sum of odd divisors of Omega(n), a(1) = 0.
%C A193512 Omega = A001222 is the number of prime divisors of the argument, counted with multiplicity.
%C A193512 a(1) = 0 by convention.
%H A193512 Antti Karttunen, <a href="/A193512/b193512.txt">Table of n, a(n) for n = 1..10000</a>
%H A193512 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A193512 a(1) = 0, for n > 1, a(n) = A000593(A001222(n)).
%F A193512 a(n) + A193511(n) = A290080(n). - _Antti Karttunen_, Jul 23 2017
%e A193512 a(8) = 4 because Omega(8) = 3 and the sum of the 2 odd divisors {1, 3} is 4.
%t A193512 Table[Total[Select[Divisors[PrimeOmega[n]], OddQ[ # ]&]], {n, 58}]
%o A193512 (PARI)
%o A193512 A000593(n) = sigma(n>>valuation(n, 2)); \\ This function from _Charles R Greathouse IV_, Sep 09 2014
%o A193512 A193512(n) = if(1==n,0,A000593(bigomega(n))); \\ _Antti Karttunen_, Jul 23 2017
%Y A193512 Cf. A000593, A001222, A193509, A193511, A290080.
%K A193512 nonn
%O A193512 1,8
%A A193512 _Michel Lagneau_, Jul 29 2011
%E A193512 Description clarified, more terms from _Antti Karttunen_, Jul 23 2017