A181700 Smallest positive integer that can be represented as the sum of n of its distinct divisors in the maximum number of ways, or a(n)=0 if no such number exists.

1, 0, 6, 2520, 48348686786400, 10543141534556403817127800577537146514577188497111149855093902265479066128013109211427715400552367011213513440000

Offset: 1

Author

William Rex Marshall, Nov 06 2010

Keywords

• nice
• nonn

Comments

A006585(n) gives the number of representations of a(n) as the sum of n of its distinct divisors.

For n >= 4, a(n) appears to coincide with A357765(n). - Max Alekseyev, Oct 09 2022

Examples

			For n=4, a(4)=2520 has the six solutions: 60+360+840+1260, 105+315+840+1260, 126+504+630+1260, 140+280+840+1260, 168+252+840+1260, 210+420+630+1260.
		

Links

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

Crossrefs

Cf. A002966, A006585, A357765.

Formula

For n >= 3, a(n) = LCM of all denominators of Egyptian fractions enumerated by A006585(n). - Max Alekseyev, Oct 12 2022

Extensions

Edited by Max Alekseyev, Oct 09 2022