A032786 - OEIS

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

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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