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 A055204 #38 Nov 17 2024 21:38:35
%S A055204 1,2,6,6,30,5,35,70,70,7,77,231,3003,858,1430,1430,24310,12155,230945,
%T A055204 46189,969969,176358,4056234,676039,676039,104006,312018,44574,
%U A055204 1292646,1077205,33393355,66786710,2203961430,64822395,90751353,90751353
%N A055204 Squarefree part of n!: n! divided by its largest square divisor.
%C A055204 Smallest number such that n!*a(n) is a square.
%H A055204 Charles R Greathouse IV, <a href="/A055204/b055204.txt">Table of n, a(n) for n = 1..3386</a> (next term has 1001 digits)
%H A055204 Kevin A. Broughan, <a href="https://www.emis.de/journals/INTEGERS/papers/c10/c10.Abstract.html">Asymptotic Order of the Square-free Part of N!</a>, Integers, 2 (2002), Article A.10.
%H A055204 Rafael Jakimczuk, <a href="https://doi.org/10.12988/imf.2017.7542">On the h-th free part of the factorial</a>, International Mathematical Forum, Vol. 12, No. 13 (2017), pp. 629-634.
%F A055204 a(n) = A007913(n!) = n!/A055071(n) = A000142(n)/A055071(n).
%F A055204 log a(n) ~ n log 2. - _Charles R Greathouse IV_, Apr 03 2012
%F A055204 sqrt(n!) = A055772(n) * sqrt(a(n)). - _Alonso del Arte_, Feb 16 2015
%e A055204 10! = 518400*7 = 7*(720)^2, so a(10) = 7.
%t A055204 f[p_, e_] := p^Mod[e, 2]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n!]; Array[a, 40] (* _Amiram Eldar_, Sep 01 2024 *)
%t A055204 a[n_] := Block[{fi = Transpose@ FactorInteger[n!]}, Times @@ (fi[[1]]^Mod[fi[[2]], 2])]; Array[a, 40] (* _Robert G. Wilson v_, Nov 17 2024 *)
%o A055204 (PARI) a(n)=core(n!) \\ _Charles R Greathouse IV_, Apr 03 2012
%Y A055204 Cf. A000142, A007913, A055071, A249831.
%K A055204 nonn
%O A055204 1,2
%A A055204 _Labos Elemer_, Jun 19 2000