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%I #8 Nov 18 2013 16:45:32
%S 1,3,3,5,5,7,7,6,6,11,11,13,13,7,5,17,17,19,19,7,11,23,23,10,13,13,9,
%T 29,29,31,31,11,17,17,7,37,37,19,13,41,41,43,43,11,23,47,47,14,14,17,
%U 17,53,53,11,11,19,29,59,59,61,61,31,8,13,13,67,67,23,23,71,71,73,73,37,19,19
%N Smallest m such that the triangular number A000217(n) divides m!.
%F a(n) = A002034(A000217(n)).
%e t(4)=10 and the first factorial divisible by 10 is 5!, so a(4)=5
%t nn=80;With[{f=Range[nn]!,trs=Accumulate[Range[nn]]},Flatten[ Table[ Position[f,_?(Divisible[#,trs[[n]]]&),{1},1],{n,nn}]]] (* _Harvey P. Dale_, Nov 18 2013 *)
%o (PARI) t(n)=n*(n+1)/2 for (n=1,50,c=1; while (c!%t(n)!=0,c++); print1(c","))
%K nonn
%O 1,2
%A _Jon Perry_, Jul 23 2003
%E Extended by _Ray Chandler_, Jun 06 2008
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