A338159 The least number which can be represented as a product of the greatest number of distinct positive integers in exactly n ways.

1, 12, 60, 96, 360, 576, 480, 15120, 864, 2880, 3360, 6912, 25200, 7680, 20160, 36960, 4320, 93312, 46080, 82944, 221760, 34560, 2494800, 311040, 53760, 88200, 15966720, 30240, 3880800, 1995840, 43200, 322560, 388800, 345600, 970200, 241920, 414720, 5832000, 529200, 5598720

Offset: 1

Author

Vladimir Letsko, Oct 14 2020

Keywords

• nonn

Comments

k = p_1^2*p_2*...*p_n obviously has exactly n required representations. Hence a(n) exists for any n.

a(n) is the least k such that A338160(k) = n.

All terms are in A025487.

Examples

			a(60) = 3 because 60 = 2*3*10 = 2*5*6 = 3*4*5 and each number less than 60 does not have exactly 3 such representations (adding the factor 1 to each product doesn't change anything).
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..1283 (first 150 terms from Dmitry Khomovsky)
• David A. Corneth, More terms

Crossrefs

Cf. A338160.

Formula

a(A338160(n)) = n.

A338160(k) <> n for k < a(n).

Extensions

a(23)-a(40) from Andrew Howroyd, Oct 14 2020