A053781 Numbers k that divide the sum of the first k composite numbers.

1, 2, 3, 7, 11, 71, 107, 115, 139, 155, 681, 1671, 4876, 21464, 30046, 311271, 788749, 10893662, 20743270, 134568163, 163879554, 920161004, 6364787032, 21400458779, 47934932406, 56133884369, 288050185452, 536023681676, 1484061538595

Offset: 1

Author

G. L. Honaker, Jr., Mar 29 2000

Keywords

• nonn

Links

• E. Friedman, What is special about this number?, see 681.

Crossrefs

Cf. A002808, A073262, A073263.

Programs

Mathematica

c = s = 0; Do[ If[ !PrimeQ[n], c++; s = s + n; If[ Mod[s, c] == 0, Print[c]]], {n, 2, 10^9}] (* Robert G. Wilson v, Nov 23 2004 *)

PARI

lista(nn) = {s = 0; n = 0; forcomposite(c=0, nn, s += c; n++; if (! (s % n), print1(n, ", ")););} \\ Michel Marcus, Mar 15 2015

Formula

Numbers k such that k divides A053767(k). - Robert G. Wilson v, Nov 24 2004

Extensions

a(19)-a(22) from Robert G. Wilson v, Nov 24 2004

a(23)-a(26) from Sean A. Irvine, Oct 01 2009

a(27)-a(29) from Donovan Johnson, Jul 06 2010