login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A056628 Largest unitary square divisor of n!. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A252485 A185589 A093159 * 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 19 09:36 EDT 2021. Contains 348074 sequences. (Running on oeis4.)