Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

In like manner if 9437056 be divided by 2 and its powers,
the quotients and their aggregate will be as below:
And if to this sum 255 be added, as in the former instance, the
aggregate will be 9363584, the first of the amicable numbers.
The first thing remarkable in these perfectly amicable numbers
is, that the number 2 and its powers are employed in the
production of all of them, and that they cannot be produced by
any other number and the powers of it. For as these amicable
numbers are images of true friendship, this most clearly shows
that such friendship can only exist between two persons.
In the next place, the numbers 3, 6, and 18, which are used
in the formation of these numbers, perspicuously indicate perfection;
and are therefore images of the perfection of true
friendship. For 3 and 6 are the first perfect numbers, the
former from being the paradigm of the all, comprehending in
itself beginning, middle and end, and the latter from being
equal to all its parts: and 18 is produced by the mu1tiplicatio.n
of 6 by 3.
In the third place, the paucity of these numbers most beautifully
adumbrates the rarity of true friendship. For between 1
and 1000 there are only two. In like manner between 284 and
20000 there are only two. And between 18416 and ten millions
there are only two.