A326126 Sum of all other divisors of n except the squarefree part of n: a(n) = sigma(n) - A007913(n).

0, 1, 1, 6, 1, 6, 1, 13, 12, 8, 1, 25, 1, 10, 9, 30, 1, 37, 1, 37, 11, 14, 1, 54, 30, 16, 37, 49, 1, 42, 1, 61, 15, 20, 13, 90, 1, 22, 17, 80, 1, 54, 1, 73, 73, 26, 1, 121, 56, 91, 21, 85, 1, 114, 17, 106, 23, 32, 1, 153, 1, 34, 97, 126, 19, 78, 1, 109, 27, 74, 1, 193, 1, 40, 121, 121, 19, 90, 1, 181, 120, 44, 1, 203, 23, 46, 33, 158, 1, 224, 21

Offset: 1

Author

Antti Karttunen, Jun 09 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537.
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000203, A007913, A326127, A326128, A326129.

Cf. also A326053, A326061, A326142.

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]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Mar 21 2024 *)

PARI

A326126(n) = (sigma(n)-core(n));

Formula

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

Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/20 = 0.4934802... . - Amiram Eldar, Mar 21 2024