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

-1, -1, -2, 2, -4, 0, -6, 5, 3, -2, -10, 13, -12, -4, -6, 14, -16, 19, -18, 17, -10, -8, -22, 30, 5, -10, 10, 21, -28, 12, -30, 29, -18, -14, -22, 54, -36, -16, -22, 40, -40, 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

Offset: 1

Author

Antti Karttunen, Jun 09 2019

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000203, A001065, A007913, A033879, A326126, A326128, A326129.

Cf. also A326143.

Programs

Mathematica

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 *)

PARI

A326127(n) = (sigma(n)-core(n)-n);

Formula

a(n) = A000203(n) - A007913(n) - n = A001065(n) - A007913(n).

a(n) = A326128(n) - A033879(n).

Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/20 - 1/2 = -0.00651977... . - Amiram Eldar, Mar 21 2024