2007-09-18 10:25:02 UTC
number is the number: 2^(2^13466918-4)*(2^13466917-1).
This is a number with about 10^4053946 digits,
(not 4053946 digits but 10^4053946 digits!!!),
but perfectly balanced, having precisely
2^(2^13466918-4)*(2^13466917-1) ordered factorizations.
* BALANCED Number?
The ancient notion of aliquot type historically (Euclid) defined by
summation of the component aliquots, and notes the three separate threads of
number so formalised. Abundant numbers have the sum of their divisors
greater than themselves, deficient numbers have the sum of their divisors
less than themselves. In the middle, with the sum of their divisors exactly
equal to the number are the "Perfect Numbers".
A redefinition in terms of the number of ordered factorisations (divisors)
for any given number (rather than the summation of the divisors) is
That is, we define the following categories in regard to the number of
Let the number of ordered factors of n be H(n), then:
a.. Deficient Ordered Factorizations ... H(n) < n
Note that this set includes the primes for which by definition H(n) = 1.
b.. Balanced Ordered Factorizations ... H(n) = n
The term balanced was used in preference to "perfect".
The first six balanced numbers are: 1, 48, 1280, 2496, 28672, 29808.
These numbers are scant and reclusive like their cousins the Perfect
Numbers. In the following analyses these are classed as abundant.
c.. Abundant Ordered Factorizations ... H(n) > n
The abundant numbers are those numbers for which
the number of ordered factors is greater than the number itself.
For further information, and graphs, see this page: