A060278 Sum of composite divisors of n less than n.

0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 10, 0, 0, 0, 12, 0, 15, 0, 14, 0, 0, 0, 30, 0, 0, 9, 18, 0, 31, 0, 28, 0, 0, 0, 49, 0, 0, 0, 42, 0, 41, 0, 26, 24, 0, 0, 70, 0, 35, 0, 30, 0, 60, 0, 54, 0, 0, 0, 97, 0, 0, 30, 60, 0, 61, 0, 38, 0, 59, 0, 117, 0, 0, 40, 42, 0, 71, 0, 98, 36, 0, 0, 127, 0, 0, 0

Offset

1,8

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

From Reinhard Zumkeller, Apr 05 2013: (Start)

a(n) = Sum_{k=2..A000005(n)-1} A010051(A027751(n,k));

a(A037143(n)) = 0;

a(A033942(n)) > 0. (End)

Maple

for n from 1 to 300 do s := 0: for j from 2 to n-1 do if isprime(j) then else if n mod j = 0 then s := s+j fi; fi: od: printf(`%d, `, s) od:

Mathematica

Join[{0}, Table[Total[Select[Most[Rest[Divisors[n]]], !PrimeQ[#]&]], {n, 2, 90}]] (* Harvey P. Dale, Oct 25 2011 *)
a[n_] := DivisorSigma[1, n] - Plus @@ FactorInteger[n][[;; , 1]] - If[PrimeQ[n], 0, n] - 1; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 20 2022 *)

Prog

(Haskell)
a060278 1 = 0
a060278 n = sum $ filter ((== 0) . a010051) $ tail $ a027751_row n
-- Reinhard Zumkeller, Apr 05 2013
(PARI) a(n) = sumdiv(n, d, if ((d<n) && (d>1) && !isprime(d), d)); \\ Michel Marcus, Jan 13 2020

Crossrefs

Cf. A000005, A000203, A010051, A027751, A033942, A035322, A035321, A037143, A023891.

Sequence in context: A105570 A327054 A101419 * A046770 A046782 A074037

Adjacent sequences: A060275 A060276 A060277 * A060279 A060280 A060281

Keyword

nonn,easy

Author

Jack Brennen, Mar 28 2001

Extensions

More terms from James A. Sellers and Matthew Conroy, Mar 29 2001

Status

approved