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Apocalyptic numbers

Source: Rioplatense Olympiad 2012, Level 3, Problem 1

August 26, 2014

number theoryprime factorizationnumber theory proposed

Problem Statement

An integer

n

is called apocalyptic if the addition of

6

different positive divisors of

n

gives

3528

. For example,

2012

is apocalyptic, because it has six divisors,

1

2

4

503

1006

and

2012

, that add up to

3528

.
Find the smallest positive apocalyptic number.