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A318675 Sum of squarefree divisors of n that have an odd number of prime factors.

%I A318675 #15 Jun 06 2025 08:34:28
%S A318675 0,2,3,2,5,5,7,2,3,7,11,5,13,9,8,2,17,5,19,7,10,13,23,5,5,15,3,9,29,
%T A318675 40,31,2,14,19,12,5,37,21,16,7,41,54,43,13,8,25,47,5,7,7,20,15,53,5,
%U A318675 16,9,22,31,59,40,61,33,10,2,18,82,67,19,26,84,71,5,73,39,8,21,18,96,79,7,3,43,83,54,22,45,32,13,89,40,20,25,34,49,24,5
%N A318675 Sum of squarefree divisors of n that have an odd number of prime factors.
%H A318675 Antti Karttunen, <a href="/A318675/b318675.txt">Table of n, a(n) for n = 1..65537</a>
%F A318675 For all n >= 1, a(n) <= A318677(n).
%F A318675 a(n) = Sum_{d|n} [A008683(d) < 0]*d.
%F A318675 a(n) = A048250(n) - A318674(n).
%F A318675 a(n) = (A048250(n) - A023900(n))/2. - _Amiram Eldar_, Jun 06 2025
%t A318675 Array[DivisorSum[#, # &, MoebiusMu@ # == -1 &] &, 96] (* _Michael De Vlieger_, Sep 04 2018 *)
%o A318675 (PARI) A318675(n) = sumdiv(n,d,(-1==moebius(d))*d);
%Y A318675 Cf. A008472, A023900, A048250, A318320, A318674, A318677.
%K A318675 nonn
%O A318675 1,2
%A A318675 _Antti Karttunen_, Sep 04 2018