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%I #22 Feb 14 2021 18:34:24
%S 1,3,16
%N Numbers k such that Sum_{j=1..k-1} (3*j)!/5^j is an integer.
%C The next term, if it exists, is greater than 1000000. - _Vaclav Kotesovec_, Sep 11 2012
%t seq={}; sum=0; fak=1; k=0; While[k<10000, sum+=fak; If[Denominator[sum]==1, AppendTo[seq,k+1]]; k++; fak*=3*k*(3*k-1)*(3*k-2)/5;]; seq
%t Select[Range[20],IntegerQ[Sum[(3k)!/5^k,{k,#-1}]]&] (* _Harvey P. Dale_, Apr 07 2019 *)
%Y Cf. A215972, A216042, A216043, A216044, A216045.
%K nonn,more,bref
%O 1,2
%A _Vaclav Kotesovec_, Sep 02 2012