Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

24575, and 301989887. And the two imperfectly amicable
numbers will be 2473599180800, and 2473901154304, the sum
of the parts of the latter of which arising from a division by
2 and its powers with the addition of unity will be equal to the
former.
Farther still, the product of 4096 multiplied by 8 will be
32768. The three numbers which are either primes or corresponding
to primes, will be 98303, 196607, and 19327352831.
And the two imperfectly or perfectly amicable numbers will be
1266618067910656, and 1266637395132416.
And in the last place if 32768 is multiplied by 8, the product
will be 262144. The three numbers which are either primes or
corresponding to primes, will be 786431, 1572863, and
1236950581247. And the two imperfectly or perfectly amicable
numbers will be 648517109391294464, and 64851 8346340827136.
In order that the reader may become acquainted with the
method of obtaining the parts of perfectly amicable numbers,
I shall give an instance of it in the two numbers 9363584 and
9437056. Let the first of these numbers then be divided by 2
and the powers of 2, viz. by 4, 8, 16, 32, 64, &c. till the division
is stopped by a remainder which is a prime number. These
quotients with the indivisible remainder will be as below,
4681792, 2340896, 1 170448, 585224, 292612, 146306, 73153. In
the next place, as the two prime numbers 191 and 383, are
multiplied together in order to produce the number 9363584,
it is evident that these also are parts of it, and consequently
they must be employed as the divisors of it. The quotient
therefore of 9363584 divided by 191 is 49024; and the quotient
of the same number divided by 383 is 24448. Each of these
quotients also may be divided by 2 and its powers. The quotients
therefore arising from the division of 49024 by 2 and
its powers are 24512, 12256, 6128, 3064, 1532, 766; and the