From: Lee Corbin (lcorbin@tsoft.com)
Date: Thu May 02 2002 - 02:16:26 MDT
Hi Spike,
> I have written a program to discover good numbers.
Are you using the sigma of N formula that depends
on knowing the factorization?
S(n) = p^(a+1)/(p-1) * q^(b+1)/(q-1) * ...
That sounds like work to first get the prime factorization,
and then multiply all those expressions!
Or are you taking the lazy way out and just grinding
out the results by considering all the divisors? (Slower,
but then it's usually better to let the machine work than
you.)
If your program isn't long, post it, and maybe there'll
be GEGNS, the Great Extropian Good Number Search. We'll
seek the megagood, gigagood, and teragood. Or as you'd
say, the good, the very good, and the double-plus good.
Lee
> -----Original Message-----
> From: owner-extropians@extropy.org
> [mailto:owner-extropians@extropy.org]On Behalf Of spike66
> Sent: Wednesday, May 01, 2002 11:14 PM
> To: extropians@extropy.org
> Subject: oh my goodness
>
>
> 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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