A032788 Numbers k such that k(k+1)(k+2)...(k+19) / (k+(k+1)+(k+2)+...+(k+19)) is an integer.

0, 1, 3, 4, 7, 8, 10, 13, 15, 16, 18, 19, 22, 23, 28, 29, 31, 33, 36, 38, 40, 43, 49, 50, 51, 53, 57, 58, 62, 64, 67, 73, 75, 76, 78, 84, 85, 88, 95, 101, 103, 106, 112, 113, 114, 118, 127, 128, 133, 135, 139, 148, 152, 153, 166, 169, 171, 172, 178, 183, 190

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• fini
• full

Comments

(d-19)/2 where d >= 19 divides 85734032330071125. In particular, the sequence is finite. - Robert Israel, Jul 13 2018

Links

• Robert Israel, Table of n, a(n) for n = 1..8739

Crossrefs

Cf. A032765-A032798.

Programs

Maple

sort([seq((t-19)/2, t=select(`>=`,numtheory:-divisors(85734032330071125),19))]); # Robert Israel, Jul 13 2018

Mathematica

Select[Range[0,190],IntegerQ[Times@@Range[#,#+19]/Total[Range[#,#+19]]]&] (* Harvey P. Dale, Sep 02 2016 *)
Select[Range[0,190],With[{c=Range[#,#+19]},Mod[Times@@c,Total[c]]==0&]] (* Harvey P. Dale, Nov 20 2024 *)

Extensions

Definition corrected by Harvey P. Dale, Sep 02 2016

Offset changed by Robert Israel, Jul 13 2018