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Numbers k such that k*(k+1)*(k+2) ... (k+13) / (k+(k+1)+(k+2)+ ... +(k+13)) is an integer.
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%I #18 Jul 13 2018 21:04:13

%S 0,1,4,6,7,10,11,13,16,21,25,26,31,32,34,39,43,46,52,54,61,65,76,78,

%T 81,88,91,106,109,115,130,131,142,151,156,169,175,186,196,208,221,241,

%U 247,256,277,286,296,331,340,351,358,403,406,416,417,439,466,481,494

%N Numbers k such that k*(k+1)*(k+2) ... (k+13) / (k+(k+1)+(k+2)+ ... +(k+13)) is an integer.

%C (d-13)/2 for divisors d>=13 of 2608781175. In particular, the sequence is finite. - _Robert Israel_, Jul 13 2018

%H Robert Israel, <a href="/A032785/b032785.txt">Table of n, a(n) for n = 1..372</a>

%p seq((t-13)/2, t=select(`>=`,numtheory:-divisors(2608781175),13)); # _Robert Israel_, Jul 13 2018

%t Select[Range[0,500],IntegerQ[Times@@Range[#,#+13]/Total[Range[ #, #+13]]]&] (* _Harvey P. Dale_, Sep 02 2016 *)

%Y Cf. A032765-A032798.

%K nonn,fini,full

%O 1,3

%A _Patrick De Geest_, May 15 1998

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