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Numbers k such that k(k+1)(k+2)...(k+19) / (k+(k+1)+(k+2)+...+(k+19)) is an integer.
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%I #25 Nov 20 2024 16:06:08

%S 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,

%T 53,57,58,62,64,67,73,75,76,78,84,85,88,95,101,103,106,112,113,114,

%U 118,127,128,133,135,139,148,152,153,166,169,171,172,178,183,190

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

%C (d-19)/2 where d >= 19 divides 85734032330071125. In particular, the sequence is finite. - _Robert Israel_, Jul 13 2018

%H Robert Israel, <a href="/A032788/b032788.txt">Table of n, a(n) for n = 1..8739</a>

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

%t Select[Range[0,190],IntegerQ[Times@@Range[#,#+19]/Total[Range[#,#+19]]]&] (* _Harvey P. Dale_, Sep 02 2016 *)

%t Select[Range[0,190],With[{c=Range[#,#+19]},Mod[Times@@c,Total[c]]==0&]] (* _Harvey P. Dale_, Nov 20 2024 *)

%Y Cf. A032765-A032798.

%K nonn,fini,full,changed

%O 1,3

%A _Patrick De Geest_, May 15 1998

%E Definition corrected by _Harvey P. Dale_, Sep 02 2016

%E Offset changed by _Robert Israel_, Jul 13 2018