cp's OEIS Frontend

A378548 Sum of divisors d of n such that n/d is odd with an even number of prime factors (counted with multiplicity).

%I A378548 #13 Dec 01 2024 10:05:10
%S A378548 1,2,3,4,5,6,7,8,10,10,11,12,13,14,16,16,17,20,19,20,22,22,23,24,26,
%T A378548 26,30,28,29,32,31,32,34,34,36,40,37,38,40,40,41,44,43,44,53,46,47,48,
%U A378548 50,52,52,52,53,60,56,56,58,58,59,64,61,62,73,64,66,68,67,68,70,72,71,80,73,74,83,76,78,80,79,80,91,82
%N A378548 Sum of divisors d of n such that n/d is odd with an even number of prime factors (counted with multiplicity).
%C A378548 Agrees with A378542 on odd n.
%C A378548 Dirichlet convolution of A000027 with A353557.
%C A378548 Dirichlet convolution of A000010 (Euler phi) with A369257.
%H A378548 Antti Karttunen, <a href="/A378548/b378548.txt">Table of n, a(n) for n = 1..20000</a>
%H A378548 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>.
%F A378548 a(n) = Sum_{d|n} A353557(n/d)*d.
%F A378548 a(n) = Sum_{d|n} A000010(n/d)*A369257(d).
%F A378548 a(n) = A000203(n) - A378549(n).
%o A378548 (PARI)
%o A378548 A353557(n) = ((n%2)&&(!(bigomega(n)%2)));
%o A378548 A378548(n) = sumdiv(n,d,d*A353557(n/d));
%Y A378548 Cf. A000010, A000203, A353557, A369257, A378526 (Dirichlet inverse), A378549.
%Y A378548 Cf. also A002131, A378542, A378546.
%K A378548 nonn
%O A378548 1,2
%A A378548 _Antti Karttunen_, Dec 01 2024