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A378544 a(n) is the sum of those divisors d of n for which A083345(d) is even, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).

%I A378544 #6 Nov 29 2024 21:04:36
%S A378544 1,1,1,1,1,1,1,1,10,1,1,13,1,1,16,17,1,10,1,21,22,1,1,13,26,1,10,29,1,
%T A378544 16,1,17,34,1,36,22,1,1,40,21,1,22,1,45,25,1,1,29,50,26,52,53,1,10,56,
%U A378544 29,58,1,1,48,1,1,31,17,66,34,1,69,70,36,1,22,1,1,41,77,78,40,1,37,91,1,1,62,86,1,88,45,1,25
%N A378544 a(n) is the sum of those divisors d of n for which A083345(d) is even, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).
%H A378544 Antti Karttunen, <a href="/A378544/b378544.txt">Table of n, a(n) for n = 1..20000</a>
%H A378544 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>.
%F A378544 a(n) = Sum_{d|n} d*A369001(d).
%F A378544 a(n) = A000203(n) - A378545(n).
%o A378544 (PARI)
%o A378544 A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
%o A378544 A369001(n) = !(A083345(n)%2);
%o A378544 A378544(n) = sumdiv(n,d,d*A369001(d));
%Y A378544 Cf. A000203, A369001, A378545.
%Y A378544 Cf. also A378444 (number of such divisors).
%K A378544 nonn
%O A378544 1,9
%A A378544 _Antti Karttunen_, Nov 29 2024