A056627 a(n) = A056622(n!).

1, 1, 1, 1, 1, 12, 12, 12, 36, 720, 720, 480, 480, 1680, 3024, 12096, 12096, 145152, 145152, 7257600, 345600, 1900800, 1900800, 136857600, 684288000, 4447872000, 4447872000, 435891456000, 435891456000, 3138418483200, 3138418483200, 6276836966400, 190207180800

Offset

1,6

Comments

Previous name "Square root of largest unitary square divisor of n!" was incorrect. See A374989 for the correct sequence with this name. - Amiram Eldar, Jul 26 2024

Links

Table of n, a(n) for n=1..33.

Formula

a(n) = A055772(n)/A055230(n) = A000188(n!)/A055229(n!).

a(n) = A056622(n!). - Michel Marcus, Aug 16 2020

a(n) = sqrt(A056628(n)). - Amiram Eldar, Jul 08 2024

Example

a(12) = A056622(12!) = A000188(12!)/A055229(12!) = 1440/3 = 480.

Mathematica

f[p_, 1] := 1; f[p_, e_] := If[EvenQ[e], p^(e/2), p^((e-3)/2)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n!]; Array[a, 33] (* Amiram Eldar, Jul 08 2024 *)

Prog

(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) = sqrtint(A056623(n!)); \\ Michel Marcus, Aug 16 2020

Crossrefs

Cf. A055772, A055230, A000188, A055229, A056622, A056628, A374989.

Sequence in context: A334245 A134324 A268914 * A334620 A061074 A372219

Adjacent sequences: A056624 A056625 A056626 * A056628 A056629 A056630

Keyword

nonn

Author

Labos Elemer, Aug 08 2000

Extensions

More terms from Michel Marcus, Aug 16 2020

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

Status

approved