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 A056628 #22 Jul 27 2024 09:42:15
%S A056628 1,1,1,1,1,144,144,144,1296,518400,518400,230400,230400,2822400,
%T A056628 9144576,146313216,146313216,21069103104,21069103104,52672757760000,
%U A056628 119439360000,3613040640000,3613040640000,18730002677760000,468250066944000000,19783565328384000000,19783565328384000000
%N A056628 a(n) = A056623(n!).
%C A056628 Previous name "Largest unitary square divisor of n!" was incorrect. See A374988 for the correct sequence with this name. - _Amiram Eldar_, Jul 26 2024
%F A056628 a(n) = A055071(n)/A055230(n)^2 = A008833(n!)/A055229(n!)^2.
%F A056628 a(n) = A056623(n!). - _Michel Marcus_, Aug 16 2020
%F A056628 a(n) = A056627(n)^2. - _Amiram Eldar_, Jul 08 2024
%e A056628 a(12) = A056623(12!) = A008833(12!)/A055229(12!)^2 = 2073600/3^2 = 230400.
%t A056628 f[p_, 1] := 1; f[p_, e_] := If[EvenQ[e], p^e, p^(e-3)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n!]; Array[a, 27] (* _Amiram Eldar_, Jul 08 2024 *)
%o A056628 (PARI)
%o A056628 A055229(n) = { my(c=core(n)); gcd(c, n/c); }; \\ _Charles R Greathouse IV_, Nov 20 2012
%o A056628 A008833(n) = n/core(n) \\ _Michael B. Porter_, Oct 17 2009
%o A056628 A056623(n) = (A008833(n)/(A055229(n)^2)); \\ _Antti Karttunen_, Nov 19 2017
%o A056628 a(n) = A056623(n!); \\ _Michel Marcus_, Aug 16 2020
%Y A056628 Cf. A055772, A055071, A055230, A000188, A008833, A055229, A056623, A056627, A374988.
%K A056628 nonn
%O A056628 1,6
%A A056628 _Labos Elemer_, Aug 08 2000
%E A056628 More terms from _Michel Marcus_, Aug 16 2020
%E A056628 Incorrect name replaced with a formula by _Amiram Eldar_, Jul 26 2024