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

1,3

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

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 *)

Crossrefs

Cf. A032765-A032798.

Sequence in context: A138971 A189750 A153144 * A338733 A210983 A213363

Adjacent sequences: A032785 A032786 A032787 * A032789 A032790 A032791

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