%I #10 Feb 01 2019 02:34:28
%S 1,1,1,2,3,4,5,6,7,8,8,10,10,11,13,14,14,15,16,17,19,19,20,21,22,23,
%T 24,25,26,27,28,29,30,31,32,34,34,35,35,37,38,39,39,41,42,43,44,45,46,
%U 47,48,49,49,51,52,53,54,55,55,57,57,59,59,61,62,63,63,64,65,67,67,69,69
%N a(n) = the largest positive integer k such that (n!/k!) has at least n divisors.
%e a(11) = 8 because 11!/8! = 9*10*11 = 990 has 24 divisors (and 24 is >= 11), but 11!/9! = 10*11 = 110 has 8 divisors (and 8 is < 11).
%p with(numtheory): a:=proc(n) local A,k: A:={}: for k from 1 to n do if tau(n!/k!)>=n then A:=A union {k} else A:=A fi od: A[nops(A)]; end: seq(a(n),n=1..90); # _Emeric Deutsch_, Mar 23 2007
%Y Cf. A128558, A128559.
%K nonn
%O 1,4
%A _Leroy Quet_, Mar 10 2007
%E More terms from _Emeric Deutsch_, Mar 23 2007