A032785 Numbers k such that k*(k+1)*(k+2) ... (k+13) / (k+(k+1)+(k+2)+ ... +(k+13)) is an integer.

0, 1, 4, 6, 7, 10, 11, 13, 16, 21, 25, 26, 31, 32, 34, 39, 43, 46, 52, 54, 61, 65, 76, 78, 81, 88, 91, 106, 109, 115, 130, 131, 142, 151, 156, 169, 175, 186, 196, 208, 221, 241, 247, 256, 277, 286, 296, 331, 340, 351, 358, 403, 406, 416, 417, 439, 466, 481, 494

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• fini
• full

Comments

(d-13)/2 for divisors d>=13 of 2608781175. In particular, the sequence is finite. - Robert Israel, Jul 13 2018

Links

• Robert Israel, Table of n, a(n) for n = 1..372

Crossrefs

Cf. A032765-A032798.

Programs

Maple

seq((t-13)/2, t=select(`>=`,numtheory:-divisors(2608781175),13)); # Robert Israel, Jul 13 2018

Mathematica

Select[Range[0,500],IntegerQ[Times@@Range[#,#+13]/Total[Range[ #, #+13]]]&] (* Harvey P. Dale, Sep 02 2016 *)

Extensions

Definition corrected by Harvey P. Dale, Sep 02 2016