A065887 Smallest number whose square is divisible by n!.

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

Cf. A000142, A019554, A055772, A065886.

Sequence in context: A003418 A109935 A347304 * A072181 A283487 A126915

Adjacent sequences: A065884 A065885 A065886 * A065888 A065889 A065890

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