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A326142 Sum of all other divisors of n except its largest squarefree divisor: a(n) = sigma(n) - A007947(n).

%I A326142 #19 Feb 28 2024 10:49:43
%S A326142 0,1,1,5,1,6,1,13,10,8,1,22,1,10,9,29,1,33,1,32,11,14,1,54,26,16,37,
%T A326142 42,1,42,1,61,15,20,13,85,1,22,17,80,1,54,1,62,63,26,1,118,50,83,21,
%U A326142 72,1,114,17,106,23,32,1,138,1,34,83,125,19,78,1,92,27,74,1,189,1,40,109,102,19,90,1,176,118,44,1,182,23,46,33
%N A326142 Sum of all other divisors of n except its largest squarefree divisor: a(n) = sigma(n) - A007947(n).
%H A326142 Antti Karttunen, <a href="/A326142/b326142.txt">Table of n, a(n) for n = 1..16384</a>
%H A326142 Antti Karttunen, <a href="/A326142/a326142.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A326142 a(n) = A000203(n) - A007947(n).
%F A326142 a(n) = n + A326143(n).
%F A326142 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A013661 - A065463 = 0.940491... . - _Amiram Eldar_, Dec 05 2023
%t A326142 rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; a[n_] := DivisorSigma[1, n] - rad[n]; Array[a, 100] (* _Amiram Eldar_, Dec 05 2023 *)
%o A326142 (PARI)
%o A326142 A007947(n) = factorback(factorint(n)[, 1]);
%o A326142 A326142(n) = (sigma(n)-A007947(n));
%Y A326142 Cf. A000203, A007947, A066503, A326143.
%Y A326142 Cf. also A326053, A326061, A326126.
%Y A326142 Cf. A013661, A065463.
%K A326142 nonn,easy
%O A326142 1,4
%A A326142 _Antti Karttunen_, Jun 09 2019