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

Author

Jack Brennen, Mar 28 2001

Keywords

• nonn
• easy

Links

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

Crossrefs

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

Programs

Haskell

a060278 1 = 0
a060278 n = sum $ filter ((== 0) . a010051) $ tail $ a027751_row n
-- Reinhard Zumkeller, Apr 05 2013

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 *)

PARI

a(n) = sumdiv(n, d, if ((d1) && !isprime(d), d)); \\ Michel Marcus, Jan 13 2020

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)

Extensions

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