A326142 Sum of all other divisors of n except its largest squarefree divisor: a(n) = sigma(n) - A007947(n).

0, 1, 1, 5, 1, 6, 1, 13, 10, 8, 1, 22, 1, 10, 9, 29, 1, 33, 1, 32, 11, 14, 1, 54, 26, 16, 37, 42, 1, 42, 1, 61, 15, 20, 13, 85, 1, 22, 17, 80, 1, 54, 1, 62, 63, 26, 1, 118, 50, 83, 21, 72, 1, 114, 17, 106, 23, 32, 1, 138, 1, 34, 83, 125, 19, 78, 1, 92, 27, 74, 1, 189, 1, 40, 109, 102, 19, 90, 1, 176, 118, 44, 1, 182, 23, 46, 33

Offset: 1

Author

Antti Karttunen, Jun 09 2019

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A000203, A007947, A066503, A326143.

Cf. also A326053, A326061, A326126.

Cf. A013661, A065463.

Programs

Mathematica

rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; a[n_] := DivisorSigma[1, n] - rad[n]; Array[a, 100] (* Amiram Eldar, Dec 05 2023 *)

PARI

A007947(n) = factorback(factorint(n)[, 1]);
A326142(n) = (sigma(n)-A007947(n));

Formula

a(n) = A000203(n) - A007947(n).

a(n) = n + A326143(n).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A013661 - A065463 = 0.940491... . - Amiram Eldar, Dec 05 2023