A108603 Numbers n such that n! can be written as the product of smaller distinct factorials in more than one way.

10, 720, 1440, 17280, 34560

Offset

1,1

Comments

No other terms < 65000. This is a subsequence of A075082. All known members of the sequence exploit the fact that 6! = 5! * 3! (they must have 6! without either 5! or 3! in one solution). Factorizations: 10 = 2*5; 720 = 2^4 * 3^2 * 5; 1440 = 2^5 * 3^2 * 5; 17280 = 2^7 * 3^3 * 5; 34560 = 2^8 * 3^3 * 5;

Links

Table of n, a(n) for n=1..5.

Example

34560! = 34559! * 6! * 4! * 2! = 34559! * 5! * 4! * 3! * 2!

Crossrefs

Cf. A075082, A000142.

Sequence in context: A174061 A058174 A006435 * A053468 A008272 A015509

Adjacent sequences: A108600 A108601 A108602 * A108604 A108605 A108606

Keyword

nonn,more

Author

Jud McCranie, Jun 13 2005

Status

approved