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A318677 Sum of divisors of n that have an odd number of prime factors (counted with multiplicity).

%I A318677 #8 Sep 05 2018 06:12:47
%S A318677 0,2,3,2,5,5,7,10,3,7,11,17,13,9,8,10,17,23,19,27,10,13,23,25,5,15,30,
%T A318677 37,29,40,31,42,14,19,12,35,37,21,16,35,41,54,43,57,53,25,47,73,7,57,
%U A318677 20,67,53,50,16,45,22,31,59,72,61,33,73,42,18,82,67,87,26,84,71,115,73,39,83,97,18,96,79,115,30,43,83,94,22,45,32
%N A318677 Sum of divisors of n that have an odd number of prime factors (counted with multiplicity).
%H A318677 Antti Karttunen, <a href="/A318677/b318677.txt">Table of n, a(n) for n = 1..65537</a>
%H A318677 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A318677 a(n) = Sum_{d|n} [A008836(d) < 0]*d.
%F A318677 a(n) = A000203(n) - A318677(n).
%F A318677 For all n >= 1, a(n) >= A318675(n).
%t A318677 Array[DivisorSum[#, # &, OddQ@ PrimeOmega@ # &] &, 87] (* _Michael De Vlieger_, Sep 04 2018 *)
%o A318677 (PARI) A318677(n) = sumdiv(n,d,(bigomega(d)%2)*d);
%Y A318677 Cf. A000203, A008836, A318675, A318676.
%K A318677 nonn
%O A318677 1,2
%A A318677 _Antti Karttunen_, Sep 04 2018