A368038 The sum of non-unitary divisors of the nonsquarefree numbers.

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

Offset

1,1

Comments

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

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... .

Mathematica

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 &]

Prog

(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]), ", "))); }

Crossrefs

Cf. A005117, A048146, A013929.

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

Cf. A002117, A013661, A072691, A229099.

Sequence in context: A256592 A256965 A191708 * A082154 A134564 A016637

Adjacent sequences: A368035 A368036 A368037 * A368039 A368040 A368041

Keyword

nonn

Author

Amiram Eldar, Dec 09 2023

Status

approved