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A342856
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Factorial numbers n that are sqrt(n)-smooth.
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0
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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
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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MATHEMATICA
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sqrtSmoothQ[n_] := FactorInteger[n][[-1, 1]] <= Sqrt[n];
Select[Range[25]!, sqrtSmoothQ]
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PROG
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(PARI) first(n) = concat(1, vector(n-1, i, (i+3)!)) \\ David A. Corneth, Apr 07 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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