A357765 Smallest positive integer that can be represented as the sum of n of its (possibly equal) divisors in the maximum number of ways (=A002966(n)).

1, 2, 12, 2520, 48348686786400, 10543141534556403817127800577537146514577188497111149855093902265479066128013109211427715400552367011213513440000

Offset: 1

Author

David A. Corneth and Max Alekseyev, Oct 12 2022

Keywords

• nice
• nonn

Examples

			a(3) = 12 since for n = 3 the tuples forming the solutions of 1 = 1/x_1 + 1/x_2 + 1/x_3 are (x_1, x_2, x_3) in {(2, 3, 6), (2, 4, 4), (3, 3, 3)}. All these terms combined have an lcm of 12. The ways to write 12 as a sum of 3 of its divisors are therefore 12 = 12/2 + 12/3 + 12/6 = 6 + 4 + 2. Similarily we have 12 = 6 + 3 + 3 and 12 = 4 + 4 + 4.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..7

Crossrefs

Apparently coincides with A181700 for n >= 4.

Cf. A002966, A006585.

Formula

a(n) = LCM of all denominators of Egyptian fractions enumerated by A002966(n).