http://qs321.pair.com?node_id=265851

in reply to Subset Sum Problem

fglock: Thanks for the link! I'm going to contact Mr.Beech, looks like he was in a similar situation.

Zaxo: Good points, but I'd like to point out a couple of things I did not mention earlier. The greater purpose here is to find "weird numbers", which are abundant and NOT semiperfect. No odd weird number is known, yet no proof of their non-existence has been formulated, so your last point is interesting.

Everyone: I am not so concerned about the factoring, much more so about testing for the lack of semi-perfection.

"Sanity is the playground of the unimaginative" -Unknown

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Re: Re: Subset Sum Problem
by Zaxo (Archbishop) on Jun 14, 2003 at 05:17 UTC

Ah! I wasn't sure how sophisticated you were or how much so you wanted to get. Now, I see you know what you want.

Since you don't care what \$n is, you may be able to select a set of factors to obtain particular properties. I think that you will have better success going at the problem from an algebraic point of view than searching numerically. These kinds of problems have usually been mined out for many digits.

After Compline,
Zaxo

Re: Re: Subset Sum Problem
by tall_man (Parson) on Jun 14, 2003 at 14:16 UTC
I think you meant to say "no odd wierd number is known." The reference Weird Number lists several even ones.

This reference to Semiperfect Numbers says that every multiple of a semiperfect number is semiperfect, which makes me think some form of sieving process would eliminate many cases quickly.

Update: I found a paper using google: Sums of Divisors and Egyptian Fractions which has some interesting results on weird numbers. Two things it mentioned are that a computer search proved there are no odd wierds below 2^32, and that all abundant numbers of the form 3^a * 5^b * 7^c are semiperfect (where a, b, c > 0).