cp's OEIS Frontend

A060278 Sum of composite divisors of n less than n.

%I A060278 #28 Jul 02 2025 16:02:01
%S A060278 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,
%T A060278 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,
%U A060278 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
%N A060278 Sum of composite divisors of n less than n.
%H A060278 Reinhard Zumkeller, <a href="/A060278/b060278.txt">Table of n, a(n) for n = 1..10000</a>
%F A060278 From _Reinhard Zumkeller_, Apr 05 2013: (Start)
%F A060278 a(n) = Sum_{k=2..A000005(n)-1} A010051(A027751(n,k));
%F A060278 a(A037143(n)) = 0;
%F A060278 a(A033942(n)) > 0. (End)
%p A060278 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:
%t A060278 Join[{0},Table[Total[Select[Most[Rest[Divisors[n]]],!PrimeQ[#]&]],{n,2,90}]] (* _Harvey P. Dale_, Oct 25 2011 *)
%t A060278 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 *)
%o A060278 (Haskell)
%o A060278 a060278 1 = 0
%o A060278 a060278 n = sum $ filter ((== 0) . a010051) $ tail $ a027751_row n
%o A060278 -- _Reinhard Zumkeller_, Apr 05 2013
%o A060278 (PARI) a(n) = sumdiv(n, d, if ((d<n) && (d>1) && !isprime(d), d)); \\ _Michel Marcus_, Jan 13 2020
%Y A060278 Cf. A000005, A000203, A010051, A027751, A033942, A035322, A035321, A037143, A023891.
%K A060278 nonn,easy
%O A060278 1,8
%A A060278 _Jack Brennen_, Mar 28 2001
%E A060278 More terms from _James Sellers_ and _Matthew Conroy_, Mar 29 2001