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Numbers k such that k(k+1)(k+2)...(k+11) / (k+(k+1)+(k+2)+...+(k+11)) is an integer.
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%I #22 Jul 13 2018 03:35:14

%S 0,2,5,7,8,11,12,17,19,22,26,32,33,35,44,47,55,62,68,77,82,89,107,110,

%T 116,117,132,143,152,176,187,197,215,242,257,264,278,297,332,341,362,

%U 407,418,440,467,539,572,602,607,656,737,782,803,845,902,957,1007,1034

%N Numbers k such that k(k+1)(k+2)...(k+11) / (k+(k+1)+(k+2)+...+(k+11)) is an integer.

%C (d-11)/2 where d>=7 is a divisor of 36018675. In particular, the sequence is finite. - _Robert Israel_, Jul 12 2018

%H Robert Israel, <a href="/A032784/b032784.txt">Table of n, a(n) for n = 1..157</a>

%p sort(convert(select(type,map(t -> (t-11)/2,numtheory:-divisors(36018675)),nonnegint),list));

%t Select[Range[0,1100],IntegerQ[Times@@Range[#,#+11]/Total[Range[#,#+11]]]&] (* _Harvey P. Dale_, Sep 02 2016 *)

%Y Cf. A032765-A032798.

%K nonn,fini,full

%O 1,2

%A _Patrick De Geest_, May 15 1998

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

%E Offset changed by _Robert Israel_, Jul 12 2018