Confused as to how the list from Jan. 23

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EBM

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Message 6 - Posted: 24 Jan 2017, 20:18:21 UTC

Hello. I recently read the list that was posted on the 23rd of January
(https://sech.me/ap/log/2017/2017-01-23/VOLUNTEERS%40BOINC.txt),

And for the numbers that are listed, their factors (as listed) do not add up to equal the other number. Now, clearly I read something from the linked Wikipedia article wrong but I don't see what. Can someone explain how the numbers on that text documents are Amicable? Thanks.
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Sergei Chernykh
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Message 8 - Posted: 24 Jan 2017, 22:56:20 UTC - in response to Message 6.  

How exactly do you "add up" factors? Can you show me it with numbers 220=2^2*5*11 and 284=2^2*71?
All pairs on that list are pairs of amicable number, that I'm sure of.
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Message 9 - Posted: 25 Jan 2017, 5:07:45 UTC - in response to Message 8.  
Last modified: 25 Jan 2017, 5:10:11 UTC

The factors of 220 are: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110
The sum of the factors is 284

The factors of 284 are: 1, 2, 4, 71, 142
The sum of the factors is 220
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Message 12 - Posted: 25 Jan 2017, 6:30:24 UTC
Last modified: 25 Jan 2017, 7:29:36 UTC

Double post
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Message 15 - Posted: 25 Jan 2017, 23:03:28 UTC - in response to Message 8.  

Thanks for replying. I saw the 220 and 284 example.
220=1,2,4,5,10,11,20,22,44,55,110 (added together, they equal 284)
284=1,2,4,71,142 (added together, they equal 220)

For example, on the text document (exactly as copied from the page; I do see that they are first written with a number raised to a power in some places but not here)

66 "BOINC: shiva, Bryan" 2017
1908798622056988970=2*5*7*11*23*11057*19661*495791 (added together, these equal 526557)
2561728891117125334=2*11*31*43*193*227*36307*54917 (added together, these equal 91731)

Shouldn't 190879...'s factors add to equal 256172, and visa versa? Thanks.
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Message 16 - Posted: 25 Jan 2017, 23:04:19 UTC - in response to Message 15.  

Is it that these are simply what you MULTIPLY to get to those numbers, and not their entire factor list?
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Message 17 - Posted: 26 Jan 2017, 0:13:13 UTC - in response to Message 16.  
Last modified: 26 Jan 2017, 0:15:47 UTC

It isn't showing ALL of the factors. If you look at the Wiki page you referenced earlier then drop down from the basic formula and look at the form of the Euler's rule. The displayed result is a amicable pair but just shown in a different format.

I'm sure there are more modern and complete theorems being used now because both models mentioned by Wiki aren't all inclusive.

Wiki states; "While these rules do generate some pairs of amicable numbers, many other pairs are known, so these rules are by no means comprehensive."
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Message 18 - Posted: 26 Jan 2017, 8:33:57 UTC - in response to Message 15.  
Last modified: 26 Jan 2017, 8:37:58 UTC

66 "BOINC: shiva, Bryan" 2017
1908798622056988970=2*5*7*11*23*11057*19661*495791 (added together, these equal 526557)
2561728891117125334=2*11*31*43*193*227*36307*54917 (added together, these equal 91731)

Shouldn't 190879...'s factors add to equal 256172, and visa versa? Thanks.

No, sum of proper divisors (a.k.a. aliquot sum) is calculated differently: https://en.wikipedia.org/wiki/Divisor_function#Definition

If you're given factorization 1908798622056988970=2*5*7*11*23*11057*19661*495791 then

s(1908798622056988970) = 3*6*8*12*24*11058*19662*495792 - 1908798622056988970 = 2561728891117125334
s(2561728891117125334) = 3*12*32*44*194*228*36308*54918 - 2561728891117125334 = 1908798622056988970
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