A032787 Numbers k such that k(k+1)(k+2)...(k+17) / (k+(k+1)+(k+2)+ ... +(k+17)) is an integer.

0, 2, 4, 5, 8, 9, 11, 14, 16, 17, 19, 23, 24, 29, 30, 32, 34, 37, 41, 44, 50, 51, 52, 54, 59, 63, 65, 68, 74, 76, 79, 85, 86, 89, 102, 104, 107, 113, 114, 119, 128, 129, 136, 140, 149, 154, 167, 170, 173, 179, 184, 194, 204, 206, 212, 219, 221, 239, 245, 254

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• fini
• full

Comments

(d-17)/2 where d >= 17 divides 131939107925625. In particular, the sequence is finite. - Robert Israel, Jul 13 2018

Links

• Robert Israel, Table of n, a(n) for n = 1..2827

Crossrefs

Cf. A032765-A032798.

Programs

Maple

sort([seq((t-17)/2, t=select(`>=`,numtheory:-divisors(131939107925625),17))]); # Robert Israel, Jul 13 2018

Mathematica

Select[Range[0,300],IntegerQ[Times@@Range[#,#+17]/Total[Range[#,#+17]]]&] (* Harvey P. Dale, Sep 02 2016 *)

Extensions

Definition corrected by Harvey P. Dale, Sep 02 2016