From: spike66 (spike66@attbi.com)
Date: Thu May 02 2002 - 00:14:20 MDT
A perfect number is one whose factors exactly
equal the number itself, examples being 6 and 28.
Another way to look at it is the ratio of the sum
of the factors to the number is unity. Thirty-nine
perfect numbers are known, all of them even.
What about odd numbers whose factor ratio is
almost unity? We could refer to those numbers
with a sum of factors ratio (goodness ratio) between
0.9 and 1.1 as good numbers. Numbers with
goodness ratio is between 0.99 and 1.01 could
be very good numbers, and goodness ratios
between 0.999 and 1.001 are damn good numbers.
Then for each order of magnitude approaching the
perfect number, we could use the usual prefixes,
kilogood, kilovery good, kilodamn good, and so on.
I have written a program to discover good numbers.
The even numbers are better, as might be expected.
For instance, 262144 has a factor sum of 262143,
for a goodness ratio of 0.9999962, making it a
kilovery good number. The best (goodest?) odd
number it has found so far is 32445 whose factor
sum is 32451 for a goodness ratio of 1.00018,
making it a damn good number, very close to the
kilogood range. And that's pretty close to perfect,
even the FRENCH judge would have to agree.
There are no known odd perfect numbers. What is the
record goodest known odd number? What if extropians
were to raise a team to do background calculations on
our confusers to search for the goodest known odd
number? We could snag the record! Who knows,
perhaps we could discover the illusive odd perfect
number.
spike
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