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URL: https://oeis.org/A065887

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A065887
Smallest number whose square is divisible by n!.
3
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
OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..735 (first 101 terms from Kevin P. Thompson)
FORMULA
a(n) = A019554(A000142(n)) = sqrt(A065886(n)) = A000142(n)/A055772(n).
EXAMPLE
a(10) = 5040 since 10! = 3628800 and the smallest square divisible by this is 25401600 = 3628800*7 = 5040^2.
MAPLE
a:= n-> mul(i[1]^ceil(i[2]/2), i=ifactors(n!)[2]):
seq(a(n), n=0..26); # Alois P. Heinz, Jan 24 2022
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Nov 27 2001
EXTENSIONS
Missing a(0) inserted, formula corrected, and a(25)-a(26) added by Kevin P. Thompson, Jan 24 2022
STATUS
approved