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A326127 a(n) = A326126(n) - n, where A326126 gives the sum of all other divisors of n except the squarefree part of n.

%I A326127 #11 Mar 21 2024 08:35:35
%S A326127 -1,-1,-2,2,-4,0,-6,5,3,-2,-10,13,-12,-4,-6,14,-16,19,-18,17,-10,-8,
%T A326127 -22,30,5,-10,10,21,-28,12,-30,29,-18,-14,-22,54,-36,-16,-22,40,-40,
%U A326127 12,-42,29,28,-20,-46,73,7,41,-30,33,-52,60,-38,50,-34,-26,-58,93,-60,-28,34,62,-46,12,-66,41,-42,4,-70,121,-72,-34,46,45,-58,12
%N A326127 a(n) = A326126(n) - n, where A326126 gives the sum of all other divisors of n except the squarefree part of n.
%H A326127 Antti Karttunen, <a href="/A326127/b326127.txt">Table of n, a(n) for n = 1..20000</a>
%F A326127 a(n) = A000203(n) - A007913(n) - n = A001065(n) - A007913(n).
%F A326127 a(n) = A326128(n) - A033879(n).
%F A326127 Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/20 - 1/2 = -0.00651977... . - _Amiram Eldar_, Mar 21 2024
%t A326127 f1[p_, e_] := (p^(e + 1) - 1)/(p - 1); f2[p_, e_] := p^Mod[e, 2]; a[n_] := Module[{f = FactorInteger[n]}, Times @@ f1 @@@ f - Times @@ f2 @@@ f - n]; a[1] = -1; Array[a, 100] (* _Amiram Eldar_, Mar 21 2024 *)
%o A326127 (PARI) A326127(n) = (sigma(n)-core(n)-n);
%Y A326127 Cf. A000203, A001065, A007913, A033879, A326126, A326128, A326129.
%Y A326127 Cf. also A326143.
%K A326127 sign
%O A326127 1,3
%A A326127 _Antti Karttunen_, Jun 09 2019