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A318674 Sum of squarefree divisors of n that have an even number of prime factors.

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%I A318674 #12 Jun 06 2025 08:34:24
%S A318674 1,1,1,1,1,7,1,1,1,11,1,7,1,15,16,1,1,7,1,11,22,23,1,7,1,27,1,15,1,32,
%T A318674 1,1,34,35,36,7,1,39,40,11,1,42,1,23,16,47,1,7,1,11,52,27,1,7,56,15,
%U A318674 58,59,1,32,1,63,22,1,66,62,1,35,70,60,1,7,1,75,16,39,78,72,1,11,1,83,1,42,86,87,88,23,1,32,92,47
%N A318674 Sum of squarefree divisors of n that have an even number of prime factors.
%H A318674 Antti Karttunen, <a href="/A318674/b318674.txt">Table of n, a(n) for n = 1..65537</a>
%F A318674 a(n) = Sum_{d|n} [A008683(d) > 0]*d.
%F A318674 a(n) = A048250(n) - A318675(n).
%F A318674 For all n >= 1, a(n) <= A318676(n).
%F A318674 a(n) = (A048250(n) + A023900(n))/2. - _Amiram Eldar_, Jun 06 2025
%t A318674 a[n_] := DivisorSum[n, # &, MoebiusMu[#] == 1 &]; Array[a, 100] (* _Amiram Eldar_, Jun 06 2025 *)
%o A318674 (PARI) A318674(n) = sumdiv(n,d,(1==moebius(d))*d);
%Y A318674 Cf. A023900, A048250, A166142, A284118, A291784, A318675, A318676.
%K A318674 nonn
%O A318674 1,6
%A A318674 _Antti Karttunen_, Sep 04 2018