This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A065887 #16 Feb 11 2024 02:39:07 %S A065887 1,1,2,6,12,60,60,420,1680,5040,5040,55440,332640,4324320,8648640, %T A065887 43243200,172972800,2940537600,8821612800,167610643200,335221286400, %U A065887 7039647014400,14079294028800,323823762662400,647647525324800,3238237626624000,6476475253248000 %N A065887 Smallest number whose square is divisible by n!. %H A065887 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 A065887 a(n) = A019554(A000142(n)) = sqrt(A065886(n)) = A000142(n)/A055772(n). %e A065887 a(10) = 5040 since 10! = 3628800 and the smallest square divisible by this is 25401600 = 3628800*7 = 5040^2. %p A065887 a:= n-> mul(i[1]^ceil(i[2]/2), i=ifactors(n!)[2]): %p A065887 seq(a(n), n=0..26); # _Alois P. Heinz_, Jan 24 2022 %t A065887 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 A065887 Cf. A000142, A019554, A055772, A065886. %K A065887 nonn %O A065887 0,3 %A A065887 _Henry Bottomley_, Nov 27 2001 %E A065887 Missing a(0) inserted, formula corrected, and a(25)-a(26) added by _Kevin P. Thompson_, Jan 24 2022