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%I #21 Jan 17 2024 09:20:06
%S 1,24,120,720,5040,40320,362880,3628800,39916800,479001600,6227020800,
%T 87178291200,1307674368000,20922789888000,355687428096000,
%U 6402373705728000,121645100408832000,2432902008176640000,51090942171709440000,1124000727777607680000
%N Factorial numbers n that are sqrt(n)-smooth.
%C According to A007917, the largest prime factor of n! is the largest prime <= n. Because the factorials grow much faster than the squares, this sequence contains the factorial numbers except 2 and 6. - _R. J. Mathar_, Apr 07 2021
%F Intersection of A000142 and A048098.
%F E.g.f.: x*(5*x^3-13*x^2+9*x+1)/(1-x)^3. - _Alois P. Heinz_, Mar 25 2021
%t sqrtSmoothQ[n_] := FactorInteger[n][[-1, 1]] <= Sqrt[n];
%t Select[Range[25]!, sqrtSmoothQ]
%o (PARI) first(n) = concat(1, vector(n-1, i, (i+3)!)) \\ _David A. Corneth_, Apr 07 2021
%Y Cf. A000142, A007917, A048098, A124657.
%K nonn
%O 1,2
%A _Jean-François Alcover_, Mar 25 2021
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