A056044 Let k be largest number such that k^2 divides n! and let m be largest number such that m! divides k; a(n) = k/m!.

1, 1, 1, 1, 1, 2, 2, 1, 3, 1, 1, 2, 2, 2, 6, 3, 3, 2, 2, 2, 2, 2, 2, 2, 10, 10, 30, 2, 2, 12, 12, 3, 3, 6, 30, 10, 10, 10, 30, 6, 6, 2, 2, 2, 30, 60, 60, 30, 210, 42, 42, 42, 42, 1, 1, 2, 2, 4, 4, 4, 4, 4, 84, 21, 21, 14, 14, 14, 42, 6, 6, 2, 2, 2, 10, 10, 70, 140, 140, 14, 126, 3, 3, 6, 30

Offset

1,6

Links

Table of n, a(n) for n=1..85.

Formula

a(n)=A000188(n!)/H!, where H!>=Floor[n/2]! is here the maximal factorial divisor.

Example

n=11, 11!=6!*6!*77 and the largest square root divisor is 6!>Floor[11/2]! a(11)=77, the quotient.

Crossrefs

A000142, A000188, A055772, A001405, A001057.

Sequence in context: A116687 A264033 A236293 * A236097 A239319 A236468

Adjacent sequences: A056041 A056042 A056043 * A056045 A056046 A056047

Keyword

nonn

Author

Labos Elemer, Jul 25 2000

Status

approved