A181700 - OEIS

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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

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OFFSET

1,3

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

LINKS

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

FORMULA

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

EXAMPLE

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.

CROSSREFS

Cf. A002966, A006585, A357765.

Sequence in context: A069643 A264801 A067630 * A199147 A097871 A210004

Adjacent sequences: A181697 A181698 A181699 * A181701 A181702 A181703

KEYWORD

nice,nonn

AUTHOR

William Rex Marshall, Nov 06 2010

EXTENSIONS

Edited by Max Alekseyev, Oct 09 2022

STATUS

approved