A056043 Let k be largest number such that k^2 divides n!; a(n) = k/floor(n/2)!.

1, 1, 1, 1, 1, 2, 2, 1, 3, 6, 6, 2, 2, 2, 6, 3, 3, 2, 2, 2, 2, 2, 2, 2, 10, 10, 30, 30, 30, 12, 12, 3, 3, 6, 30, 10, 10, 10, 30, 6, 6, 2, 2, 2, 30, 60, 60, 30, 210, 42, 42, 42, 42, 28, 28, 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, 126

Offset

1,6

Links

Table of n, a(n) for n=1..82.

Formula

a(n) = A000188(n!)/floor(n/2)! = A055772(n)/(A000142(A001057(n))^2.

Example

n=7, 7! = 5040 = 144*35, so 12 is its largest square-root-divisor, A000188(5040) and it is divisible by 6=3! and a(7)=2, the quotient, 12/3!.

Crossrefs

Cf. A000142, A000188, A001057, A055772, A001405.

Sequence in context: A110858 A008279 A239572 * A187005 A158497 A334894

Adjacent sequences: A056040 A056041 A056042 * A056044 A056045 A056046

Keyword

nonn

Author

Labos Elemer, Jul 25 2000

Status

approved