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%I #20 Jul 14 2018 02:34:20
%S 0,1,4,7,9,14,19,21,28,34,49,70,84,109,119,154,217,259,364,609,784,
%T 1099,1834,5509
%N Numbers k such that k*(k+1)*(k+2)*...*(k+7) / (k+(k+1)+(k+2)+...+(k+7)) is an integer.
%C (d-7)/2 where d >= 7 is a divisor of 11025, so sequence is finite. - _Robert Israel_, Jul 12 2018
%t Select[Range[0, 300], IntegerQ[Times@@Range[#, # + 7] / Total[Range[#, # + 7]]] &] (* _Vincenzo Librandi_, Jul 13 2018 *)
%Y Cf. A032777, A032779.
%K nonn,fini,full
%O 1,3
%A _Patrick De Geest_, May 15 1998
%E Offset changed by _Robert Israel_, Jul 12 2018
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