%I #8 Dec 09 2023 07:08:36

%S 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,

%T 36,105,20,40,84,39,64,72,54,48,120,21,36,87,84,140,112,60,42,144,11,

%U 64,30,72,126,96,72,108,96,233,28,76,60,120,54,112,180,117,84

%N The sum of non-unitary divisors of the nonsquarefree numbers.

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

%H Amiram Eldar, <a href="/A368038/b368038.txt">Table of n, a(n) for n = 1..10000</a>

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

%F 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... .

%t 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 &]

%o (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]), ", ")));}

%Y Cf. A005117, A048146, A013929.

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

%Y Cf. A002117, A013661, A072691, A229099.

%K nonn

%O 1,1

%A _Amiram Eldar_, Dec 09 2023