A032784 Numbers k such that k(k+1)(k+2)...(k+11) / (k+(k+1)+(k+2)+...+(k+11)) is an integer.

0, 2, 5, 7, 8, 11, 12, 17, 19, 22, 26, 32, 33, 35, 44, 47, 55, 62, 68, 77, 82, 89, 107, 110, 116, 117, 132, 143, 152, 176, 187, 197, 215, 242, 257, 264, 278, 297, 332, 341, 362, 407, 418, 440, 467, 539, 572, 602, 607, 656, 737, 782, 803, 845, 902, 957, 1007, 1034

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• fini
• full

Comments

(d-11)/2 where d>=7 is a divisor of 36018675. In particular, the sequence is finite. - Robert Israel, Jul 12 2018

Links

• Robert Israel, Table of n, a(n) for n = 1..157

Crossrefs

Cf. A032765-A032798.

Programs

Maple

sort(convert(select(type,map(t -> (t-11)/2,numtheory:-divisors(36018675)),nonnegint),list));

Mathematica

Select[Range[0,1100],IntegerQ[Times@@Range[#,#+11]/Total[Range[#,#+11]]]&] (* Harvey P. Dale, Sep 02 2016 *)

Extensions

Definition corrected by Harvey P. Dale, Sep 02 2016

Offset changed by Robert Israel, Jul 12 2018