A023891 Sum of composite divisors of n.

0, 0, 0, 4, 0, 6, 0, 12, 9, 10, 0, 22, 0, 14, 15, 28, 0, 33, 0, 34, 21, 22, 0, 54, 25, 26, 36, 46, 0, 61, 0, 60, 33, 34, 35, 85, 0, 38, 39, 82, 0, 83, 0, 70, 69, 46, 0, 118, 49, 85, 51, 82, 0, 114, 55, 110, 57, 58, 0, 157, 0, 62, 93, 124, 65, 127, 0, 106, 69, 129, 0

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203, A035322, A035321, A060278, A023890.

Programs

Mathematica

Array[ Plus @@ (Select[ Divisors[ # ], (!PrimeQ[ # ] && #>1)& ])&, 75 ]
a[n_] := DivisorSigma[1, n] - Plus @@ FactorInteger[n][[;; , 1]] - 1; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 20 2022 *)

PARI

a(n) = sumdiv(n, d, d*!isprime(d)) - 1; \\ Michel Marcus, Jun 12 2019

Formula

a(n) = A023890(n) - 1. - Sean A. Irvine, Jun 11 2019