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Old 2012-03-24, 01:51   #12
schickel
 
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Quote:
Originally Posted by Dubslow View Post
Alright, I'm trying not to bug anybody and read the already-posted questions, but the link above that's supposed to talk about drivers and guides etc. is down, and the wiki, while like Wikipedia is good for explaining if you already know it, it isn't much use to me.
You're right: the whole Getting Started sticky could use a revamp.
Quote:
(Why would 6 being a factor of a term mean that the next term will be higher?)
Maybe this will help. A) 6 is a perfect number; and B) an abundant number has a sigma that is higher than itself. Put those two things together with this and you've got your answer:
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Originally Posted by Wikipedia
Every proper multiple of a perfect number, and every multiple of an abundant number, is abundant.
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It appears that the lafn.org links in general are all down, however the domain's homepage works fine.
Yes, I'm starting to be concerned there. The last message I had from Clifford was on 1/29 in response to a message I sent on 12/29. I sent emails to both addresses I had for him since then with no reply.....in the meantime I redirected the Analysis link to The Wayback Machine, but I wonder if we should rehost the info he had posted.
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Old 2012-03-24, 02:02   #13
Dubslow
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Originally Posted by schickel View Post
....in the meantime I redirected the Analysis link to The Wayback Machine, but I wonder if we should rehost the info he had posted.
That's a great idea, I can't believe I didn't think of that. And thanks for stooping to my math level; unfortunately, discrete math/number theory has never really appealed to me (still doesn't, to be honest), but GIMPS is such an awesome DC project. Now that I'm here though, it seems interesting, but I need to fill in the mathematics Thanks for helping.

(Among other deficiencies is a complete lack of knowledge of factoring methods besides ECM, of which I only have a basic idea that it's similar to P-1 and uses elliptic curves. I've gleaned that the first line of attack is ECM, but I'm not sure when to switch methods or what to use. You got any more links? :P)
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Old 2016-01-16, 23:33   #14
Bode Didymos
 
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Default About the starting value of an Aliquot Sequence

I have question about the starting value of a aliquot sequence. OP said that an Aliquot sequences are generally referred to by their starting value, is there some numbers that start an Aliquot Sequence but is never in the middle of another aliquot sequence? how do you call those numbers? these numbers would be those that are not in the image of the aliquot sum function. Another related question, if such "patriarch numbers" exist (or what ever you call them), does every branch of an aliquot family tree have a "patriarch" that initiate that branch or its goes on and on indefinitely?

Thank you for your time =D
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Old 2016-01-17, 10:45   #15
Happy5214
 
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I will answer the first part of your question and try to come up with something for the second part. An untouchable number is a number that does not occur as the aliquot sum of any other number. There are infinitely many untouchable numbers, it is conjectured that only one is odd (5), and it is also believed that all but 2 and 5 are composite. This is a list of untouchable numbers below 700.

The second part is a little trickier. I would imagine that every full sequence branches from an untouchable number. (Could someone more knowledgeable confirm that?) But don't confuse that untouchable number with the starting value we use. We basically refer to sequences by their lowest value. For example, 564 is used as a starting value, but it is not an untouchable number as it is the aliquot sum of 563^2. Also, it is conjectured, but not yet proven, that all sequences terminate with a prime, perfect number, or aliquot cycle. There could be infinitely long sequences that never terminate. So that answer to both parts of your second question could be "yes."
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Old 2016-01-18, 13:58   #16
henryzz
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Quote:
Originally Posted by Happy5214 View Post
I will answer the first part of your question and try to come up with something for the second part. An untouchable number is a number that does not occur as the aliquot sum of any other number. There are infinitely many untouchable numbers, it is conjectured that only one is odd (5), and it is also believed that all but 2 and 5 are composite. This is a list of untouchable numbers below 700.

The second part is a little trickier. I would imagine that every full sequence branches from an untouchable number. (Could someone more knowledgeable confirm that?) But don't confuse that untouchable number with the starting value we use. We basically refer to sequences by their lowest value. For example, 564 is used as a starting value, but it is not an untouchable number as it is the aliquot sum of 563^2. Also, it is conjectured, but not yet proven, that all sequences terminate with a prime, perfect number, or aliquot cycle. There could be infinitely long sequences that never terminate. So that answer to both parts of your second question could be "yes."
I think that stating that every sequence starts at an untouchable number might be similar to stating that all sequences terminate as you could just as easily have an infinite sequence backward as forwards.
I would guess that it would be much less likely to happen as numbers in general get bigger as you go upward in a sequence and smaller as you go down. Numbers are limited in how much they can go down so it is less likely to happen.
We do get long sequences reaching smaller numbers than their starting value(i.e. merging with a smaller sequence).
Need to get on with work now. Might think more later.

Last fiddled with by henryzz on 2016-01-18 at 13:58
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