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A065887
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Smallest number whose square is divisible by n!.
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3
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1, 1, 2, 6, 12, 60, 60, 420, 1680, 5040, 5040, 55440, 332640, 4324320, 8648640, 43243200, 172972800, 2940537600, 8821612800, 167610643200, 335221286400, 7039647014400, 14079294028800, 323823762662400, 647647525324800, 3238237626624000, 6476475253248000
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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a(10) = 5040 since 10! = 3628800 and the smallest square divisible by this is 25401600 = 3628800*7 = 5040^2.
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MAPLE
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a:= n-> mul(i[1]^ceil(i[2]/2), i=ifactors(n!)[2]):
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MATHEMATICA
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f[p_, e_] := p^Ceiling[e/2]; a[0] = a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n!]; Array[a, 30, 0] (* Amiram Eldar, Feb 11 2024 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Missing a(0) inserted, formula corrected, and a(25)-a(26) added by Kevin P. Thompson, Jan 24 2022
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STATUS
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approved
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