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

Author

Jud McCranie, Jun 13 2005

Keywords

• nonn
• more

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;

Examples

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

Crossrefs

Cf. A075082, A000142.