A032786 Numbers k such that k(k+1)(k+2)...(k+15) / (k+(k+1)+(k+2)+...+(k+15)) is an integer.

0, 3, 5, 6, 9, 10, 12, 15, 17, 20, 24, 25, 30, 31, 33, 38, 42, 45, 51, 53, 55, 60, 64, 66, 75, 77, 80, 87, 90, 105, 108, 114, 115, 129, 130, 141, 150, 155, 168, 174, 180, 185, 195, 207, 213, 220, 240, 246, 255, 262, 276, 285, 295, 305, 311, 330, 339, 350, 357

Offset

1,2

Comments

(d-15)/2 where d >= 15 divides 4108830350625. In particular, the sequence is finite. - Robert Israel, Jul 13 2018

Links

Robert Israel, Table of n, a(n) for n = 1..1208

Maple

sort([seq((t-15)/2, t=select(`>=`, numtheory:-divisors(4108830350625), 15))]); # Robert Israel, Jul 13 2018

Mathematica

Select[Range[0, 500], IntegerQ[Times@@Range[#, #+15]/Total[Range[ #, #+15]]]&] (* Harvey P. Dale, Sep 02 2016 *)

Crossrefs

Cf. A032765-A032798.

Sequence in context: A080307 A001969 A075311 * A080309 A281746 A287162

Adjacent sequences: A032783 A032784 A032785 * A032787 A032788 A032789

Keyword

nonn,fini,full

Author

Patrick De Geest, May 15 1998

Extensions

Definition corrected by Harvey P. Dale, Sep 02 2016

Offset changed by Robert Israel, Jul 13 2018

Status

approved