A056628 Largest unitary square divisor of 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

1,6

Comments

Unitary analog of A055071.

Links

Table of n, a(n) for n=1..27.

Formula

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

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

Example

n=12, 12!=1440*1440*231, the largest square divisor is 1440^2=2073600. It becomes unitary if divided by g^2=9, so a(12)=230400=480^2.

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

Crossrefs

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

Sequence in context: A185589 A093159 A350453 * A093769 A124512 A199546

Adjacent sequences: A056625 A056626 A056627 * A056629 A056630 A056631

Keyword

nonn

Author

Labos Elemer, Aug 08 2000

Extensions

More terms from Michel Marcus, Aug 16 2020

Status

approved