A035322 -id:A035322 - cp's OEIS frontend

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

Jack Brennen, Mar 28 2001

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

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

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

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:

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 *)

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

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)

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

A023891 Sum of composite divisors of n.

Original entry on oeis.org

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

Olivier Gérard

nonn

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

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

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 *)

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

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

A035321 Sum of composite divisors of n that are not primes nor prime powers.

Original entry on oeis.org

0, 0, 0, 0, 0, 6, 0, 0, 0, 10, 0, 18, 0, 14, 15, 0, 0, 24, 0, 30, 21, 22, 0, 42, 0, 26, 0, 42, 0, 61, 0, 0, 33, 34, 35, 72, 0, 38, 39, 70, 0, 83, 0, 66, 60, 46, 0, 90, 0, 60, 51, 78, 0, 78, 55, 98, 57, 58, 0, 153, 0, 62, 84, 0, 65, 127, 0, 102, 69, 129, 0, 168, 0, 74, 90, 114, 77

Offset: 1

N. J. A. Sloane

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000203, A035322, A023891, A060278.

One less than A178637.

pp := array(1..100); for i from 1 to 100 do pp[i] := 0; od: for i from 1 to 25 do for j from 1 to 6 do t1 := ithprime(i)^j; if t1<100 then pp[t1] := 1; fi; od: od: pp[1] := 1; A035321 := proc(n) local i,d,t1,t2; t1 := 0; for d from 1 to n do if n mod d = 0 and pp[d] = 0 then t1 := t1+d; fi; od; t1; end;

Array[ Plus @@ (Select[ Divisors[ # ], (Length[ FactorInteger[ # ] ]>1)& ])&, 80 ]

A035321(n) = sumdiv(n,d,(omega(d)>1)*(d)); \\ Antti Karttunen, Aug 06 2018

a(n) = A178637(n) - 1. - Antti Karttunen, Aug 06 2018

Description corrected by Jack Brennen, Mar 28 2001

cp's OEIS Frontend

A060278 Sum of composite divisors of n less than n.

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A023891 Sum of composite divisors of n.

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A035321 Sum of composite divisors of n that are not primes nor prime powers.

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