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A378543 Sum of divisors d of n such that n/d has an odd number of prime factors (counted with multiplicity).

%I A378543 #11 Dec 01 2024 10:05:06
%S A378543 0,1,1,2,1,5,1,5,3,7,1,11,1,9,8,10,1,16,1,15,10,13,1,25,5,15,10,19,1,
%T A378543 32,1,21,14,19,12,35,1,21,16,35,1,42,1,27,25,25,1,51,7,36,20,31,1,50,
%U A378543 16,45,22,31,1,72,1,33,31,42,18,62,1,39,26,60,1,80,1,39,41,43,18,72,1,71,30,43,1,94,22,45,32,65
%N A378543 Sum of divisors d of n such that n/d has an odd number of prime factors (counted with multiplicity).
%C A378543 Agrees with A378549 on odd n.
%C A378543 Dirichlet convolution of A000027 with A066829.
%C A378543 Dirichlet convolution of A000010 (Euler phi) with A056924.
%H A378543 Antti Karttunen, <a href="/A378543/b378543.txt">Table of n, a(n) for n = 1..20000</a>
%H A378543 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>.
%F A378543 a(n) = Sum_{d|n} A066829(n/d)*d.
%F A378543 a(n) = Sum_{d|n} A000010(n/d)*A056924(d).
%F A378543 a(n) = A000203(n) - A378543(n).
%o A378543 (PARI) A378543(n) = sumdiv(n,d,d*!!(bigomega(n/d)%2));
%Y A378543 Cf. A000010, A000027, A000203, A056924, A066829, A378542.
%Y A378543 Cf. also A378547, A378549.
%K A378543 nonn
%O A378543 1,4
%A A378543 _Antti Karttunen_, Dec 01 2024