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%I #16 Feb 11 2024 02:39:07
%S 1,1,2,6,12,60,60,420,1680,5040,5040,55440,332640,4324320,8648640,
%T 43243200,172972800,2940537600,8821612800,167610643200,335221286400,
%U 7039647014400,14079294028800,323823762662400,647647525324800,3238237626624000,6476475253248000
%N Smallest number whose square is divisible by n!.
%H Alois P. Heinz, <a href="/A065887/b065887.txt">Table of n, a(n) for n = 0..735</a> (first 101 terms from Kevin P. Thompson)
%F a(n) = A019554(A000142(n)) = sqrt(A065886(n)) = A000142(n)/A055772(n).
%e a(10) = 5040 since 10! = 3628800 and the smallest square divisible by this is 25401600 = 3628800*7 = 5040^2.
%p a:= n-> mul(i[1]^ceil(i[2]/2), i=ifactors(n!)[2]):
%p seq(a(n), n=0..26); # _Alois P. Heinz_, Jan 24 2022
%t 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 *)
%Y Cf. A000142, A019554, A055772, A065886.
%K nonn
%O 0,3
%A _Henry Bottomley_, Nov 27 2001
%E Missing a(0) inserted, formula corrected, and a(25)-a(26) added by _Kevin P. Thompson_, Jan 24 2022
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