A342856 - OEIS

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A342856

Factorial numbers n that are sqrt(n)-smooth.

1, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000, 51090942171709440000, 1124000727777607680000

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OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..20.

FORMULA

Intersection of A000142 and A048098.

E.g.f.: x*(5*x^3-13*x^2+9*x+1)/(1-x)^3. - Alois P. Heinz, Mar 25 2021

MATHEMATICA

sqrtSmoothQ[n_] := FactorInteger[n][[-1, 1]] <= Sqrt[n];

Select[Range[25]!, sqrtSmoothQ]

PROG

(PARI) first(n) = concat(1, vector(n-1, i, (i+3)!)) \\ David A. Corneth, Apr 07 2021

CROSSREFS

Cf. A000142, A007917, A048098, A124657.