Amicable pairs and what must be a stupid question

Message boards : Random stuff : Amicable pairs and what must be a stupid question

To post messages, you must log in.

AuthorMessage
Henrik Nilsson

Send message
Joined: 27 Apr 17
Posts: 9
Credit: 16,243,969
RAC: 0
   
Message 572 - Posted: 11 Jul 2017, 22:22:58 UTC

Hi,

Pardon me for asking what must be a stupid question. I suppose I'm getting the notation wrong.

Regarding the amicable pair:

22559194686624505630=2*5*7*23*61*99643*2305266221
26660358080018237666=2*7*13*159773*523681*1750751

The factors of 22559194686624505630 do not sum up to 2666035808001823766, and the factors of 26660358080018237666 do not sum up to 22559194686624505630. What, then, makes this pair amicable?
ID: 572 · Rating: 0 · rate: Rate + / Rate - Report as offensive    Reply Quote
Sergei Chernykh
Project administrator
Project developer

Send message
Joined: 5 Jan 17
Posts: 455
Credit: 72,451,573
RAC: 0
   
Message 573 - Posted: 12 Jul 2017, 6:12:47 UTC
Last modified: 12 Jul 2017, 6:13:43 UTC

ID: 573 · Rating: 0 · rate: Rate + / Rate - Report as offensive    Reply Quote
Henrik Nilsson

Send message
Joined: 27 Apr 17
Posts: 9
Credit: 16,243,969
RAC: 0
   
Message 574 - Posted: 12 Jul 2017, 9:40:43 UTC - in response to Message 573.  

I see. Thanks!

Is there, then, an easy way to list all the proper divisors of these numbers? (But yes, I can see why you choose to list only the factors.)
ID: 574 · Rating: 0 · rate: Rate + / Rate - Report as offensive    Reply Quote
Sergei Chernykh
Project administrator
Project developer

Send message
Joined: 5 Jan 17
Posts: 455
Credit: 72,451,573
RAC: 0
   
Message 575 - Posted: 12 Jul 2017, 10:08:16 UTC - in response to Message 574.  
Last modified: 12 Jul 2017, 10:10:56 UTC

I see. Thanks!

Is there, then, an easy way to list all the proper divisors of these numbers? (But yes, I can see why you choose to list only the factors.)

There is a formula to calculate sum of all proper divisors based on factorization: https://en.wikipedia.org/wiki/Divisor_function#Properties
For your case, s(22559194686624505630) = (2+1)*(5+1)*(7+1)*(23+1)*(61+1)*(99643+1)*(2305266221+1) - 22559194686624505630 = 26660358080018237666
ID: 575 · Rating: 0 · rate: Rate + / Rate - Report as offensive    Reply Quote

Message boards : Random stuff : Amicable pairs and what must be a stupid question


©2021 Sergei Chernykh