A360590 a(n) is the smallest number which can be represented as the product of n distinct integers > 1 in exactly n ways.

2, 12, 60, 420, 3456, 60060, 155520, 1512000, 13063680, 169344000, 1524096000, 16765056000, 217945728000, 3705077376000, 52306974720000, 889218570240000, 16895152834560000, 328655183560704000, 6244448487653376000, 143622315216027648000, 2922401892221779968000, 67215243521100939264000

Offset: 1

Author

Ilya Gutkovskiy, Feb 12 2023

Keywords

• nonn

Examples

			For n = 2: 12 = 2 * 6 = 3 * 4.
For n = 3: 60 = 2 * 3 * 10 = 2 * 5 * 6 = 3 * 4 * 5.
For n = 4: 420 = 2 * 3 * 5 * 14 = 2 * 3 * 7 * 10 = 2 * 5 * 6 * 7 = 3 * 4 * 5 * 7.
		

Links

• Eric Weisstein's World of Mathematics, Unordered Factorization

Crossrefs

Cf. A045778, A330974.

Extensions

a(7)-a(10) from Daniel Suteu, Feb 13 2023

a(11)-a(22) from Bert Dobbelaere, Feb 16 2023