A056627 Square root of largest unitary square divisor of 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

Unitary analog of A055772.

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

Example

n=12, 12!=1440*1440*231, square root of the largest square divisor is 1440, but it becomes unitary if divided by g=3, so a(12)=480.

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.

Sequence in context: A334245 A134324 A268914 * A334620 A061074 A064161

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

Status

approved