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A378545 a(n) is the sum of those divisors d of n for which A083345(d) is odd, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).

%I A378545 #7 Nov 29 2024 21:04:41
%S A378545 0,2,3,6,5,11,7,14,3,17,11,15,13,23,8,14,17,29,19,21,10,35,23,47,5,41,
%T A378545 30,27,29,56,31,46,14,53,12,69,37,59,16,69,41,74,43,39,53,71,47,95,7,
%U A378545 67,20,45,53,110,16,91,22,89,59,120,61,95,73,110,18,110,67,57,26,108,71,173,73,113,83,63,18,128,79,149
%N A378545 a(n) is the sum of those divisors d of n for which A083345(d) is odd, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).
%H A378545 Antti Karttunen, <a href="/A378545/b378545.txt">Table of n, a(n) for n = 1..20000</a>
%H A378545 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>.
%F A378545 a(n) = Sum_{d|n} d*A377874(d).
%F A378545 a(n) = A000203(n) - A378544(n).
%o A378545 (PARI)
%o A378545 A377874(n) = { my(f=factor(n)); (numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1])))%2); };
%o A378545 A378545(n) = sumdiv(n,d,d*A377874(d));
%Y A378545 Cf. A000203, A377874, A378544.
%Y A378545 Cf. also A378445 (number of such divisors).
%K A378545 nonn
%O A378545 1,2
%A A378545 _Antti Karttunen_, Nov 29 2024