Amiram Eldar, <a href="/A368038/b368038_1.txt">Table of n, a(n) for n = 1..10000</a>

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OEIS Server: Installed first b-file as b368038.txt.

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Amiram Eldar, <a href="/A368038/b368038_1.txt">Table of n, a(n) for n = 1..10000</a>

allocatedThe sum of non-unitary divisors of forthe Amiramnonsquarefree Eldarnumbers.

2, 6, 3, 8, 14, 9, 12, 24, 5, 12, 16, 30, 41, 36, 24, 18, 56, 7, 15, 28, 36, 48, 48, 24, 62, 36, 105, 20, 40, 84, 39, 64, 72, 54, 48, 120, 21, 36, 87, 84, 140, 112, 60, 42, 144, 11, 64, 30, 72, 126, 96, 72, 108, 96, 233, 28, 76, 60, 120, 54, 112, 180, 117, 84

1,1

The positive terms of A048146, since A048146(k) = 0 if and only if k is squarefree (A005117).

a(n) = A048146(A013929(n)).

Sum_{k=1..n} a(k) ~ c * n^2, where c = (zeta(2)/2)*(1-1/zeta(3))/(1-1/zeta(2))^2 = 0.899359898779... .

f[p_, e_] := (p^(e+1)-1)/(p-1); nusigma[n_] := Module[{fct = FactorInteger[n]}, If[n == 1, 0, Times @@ f @@@ fct - Times @@ (1 + Power @@@ fct)]]; Select[Array[nusigma, 200], # > 0 &]

(PARI) lista(kmax) = {my(f); for(k = 1, kmax, f = factor(k); if(!issquarefree(f), print1(sigma(f) - prod(i=1, #f~, 1+f[i, 1]^f[i, 2]), ", "))); }

Cf. A005117, A048146, A013929.

Cf. A084936, A174961, A275699, A368039, A368040.

Cf. A002117, A013661, A072691, A229099.

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Amiram Eldar, Dec 09 2023

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allocated for Amiram Eldar

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