A234540 Nonprimes k that divide the sum of the nonprimes up to k.

1, 22, 25, 118, 414, 2745, 10623, 63201, 1039161, 1693864, 2285297, 52962021, 66998865, 232974402, 315796805, 336125877, 834972771, 1233903294, 1309750075, 1617454215, 2056836133, 5455816485, 8589896196, 9030058217, 10622144467, 12324258770, 33725308558

Offset: 1

Author

Vicente Izquierdo Gomez, Dec 27 2013

Keywords

• nonn

Comments

Standard heuristics suggest that this sequence is infinite. - Charles R Greathouse IV, Dec 29 2013

Examples

			a(2) = 22 because 1 + 4 + 6 + 8 + 9 + 10 + ... + 22 = 176 and 176/22 = 8.
		

Crossrefs

Cf. A007506.

Programs

Mathematica

s = 0; Do[If[PrimeQ[k], Continue[]]; s += k; If[Mod[s, k] == 0, Print[k]], {k, 10^10}] (* Gomez *)
Select[Range[10^4], Not[PrimeQ[#]] && Divisible[Sum[Boole[Not[PrimeQ[m]]]m, {m, #}], #] &] (* Alonso del Arte, Dec 29 2013 *)

PARI

v=List([s=1]); forcomposite(n=4,1e9,if(s%n==0, listput(v,n)); s+=n); Vec(v) \\ Charles R Greathouse IV, Dec 29 2013

Extensions

a(14)-a(27) from Donovan Johnson, Dec 30 2013