A056628 a(n) = A056623(n!).

1, 1, 1, 1, 1, 144, 144, 144, 1296, 518400, 518400, 230400, 230400, 2822400, 9144576, 146313216, 146313216, 21069103104, 21069103104, 52672757760000, 119439360000, 3613040640000, 3613040640000, 18730002677760000, 468250066944000000, 19783565328384000000, 19783565328384000000

Offset: 1

Author

Labos Elemer, Aug 08 2000

Keywords

• nonn

Comments

Previous name "Largest unitary square divisor of n!" was incorrect. See A374988 for the correct sequence with this name. - Amiram Eldar, Jul 26 2024

Examples

			a(12) = A056623(12!) = A008833(12!)/A055229(12!)^2 = 2073600/3^2 = 230400.
		

Crossrefs

Cf. A055772, A055071, A055230, A000188, A008833, A055229, A056623, A056627, A374988.

Programs

Mathematica

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 *)

PARI

A055229(n) = { my(c=core(n)); gcd(c, n/c); }; \\ Charles R Greathouse IV, Nov 20 2012
A008833(n) = n/core(n) \\ Michael B. Porter, Oct 17 2009
A056623(n) = (A008833(n)/(A055229(n)^2)); \\ Antti Karttunen, Nov 19 2017
a(n) = A056623(n!); \\ Michel Marcus, Aug 16 2020

Formula

a(n) = A055071(n)/A055230(n)^2 = A008833(n!)/A055229(n!)^2.

a(n) = A056623(n!). - Michel Marcus, Aug 16 2020

a(n) = A056627(n)^2. - Amiram Eldar, Jul 08 2024

Extensions

More terms from Michel Marcus, Aug 16 2020

Incorrect name replaced with a formula by Amiram Eldar, Jul 26 2024