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A378549 Sum of divisors d of n such that n/d is not an odd number with an even number of prime factors (counted with multiplicity).

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%I A378549 #9 Dec 01 2024 10:05:14
%S A378549 0,1,1,3,1,6,1,7,3,8,1,16,1,10,8,15,1,19,1,22,10,14,1,36,5,16,10,28,1,
%T A378549 40,1,31,14,20,12,51,1,22,16,50,1,52,1,40,25,26,1,76,7,41,20,46,1,60,
%U A378549 16,64,22,32,1,104,1,34,31,63,18,76,1,58,26,72,1,115,1,40,41,64,18,88,1,106,30,44,1,136,22,46,32
%N A378549 Sum of divisors d of n such that n/d is not an odd number with an even number of prime factors (counted with multiplicity).
%C A378549 Agrees with A378543 on odd n.
%H A378549 Antti Karttunen, <a href="/A378549/b378549.txt">Table of n, a(n) for n = 1..20000</a>
%H A378549 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>.
%F A378549 a(n) = Sum_{d|n} (1-A353557(d))*(n/d).
%F A378549 a(n) = A000203(n) - A378548(n).
%o A378549 (PARI)
%o A378549 A353557(n) = ((n%2)&&(!(bigomega(n)%2)));
%o A378549 A378549(n) = sumdiv(n,d,(1-A353557(d))*(n/d));
%Y A378549 Cf. A000203, A353557, A378548.
%Y A378549 Cf. also A378543, A378547.
%K A378549 nonn
%O A378549 1,4
%A A378549 _Antti Karttunen_, Dec 01 2024