What are Amicable numbers ?

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Alez
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#1 What are Amicable numbers ?

Unread post by Alez » Sun Jan 29, 2017 12:53 am

Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number. (A proper divisor of a number is a positive factor of that number other than the number itself. For example, the proper divisors of 6 are 1, 2, and 3.) A pair of amicable numbers constitutes an aliquot sequence of period 2. A related concept is that of a perfect number, which is a number that equals the sum of its own proper divisors, in other words a number which forms an aliquot sequence of period 1. Numbers that are members of an aliquot sequence with period greater than 2 are known as sociable numbers.

The smallest pair of amicable numbers is (220, 284). They are amicable because the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.

The first ten amicable pairs are: (220, 284), (1184, 1210), (2620, 2924), (5020, 5564), (6232, 6368), (10744, 10856), (12285, 14595), (17296, 18416), (63020, 76084), and (66928, 66992).(sequence A259180 in the OEIS). (Also see OEIS A002025 and OEIS A002046)

Further information available on this Wiki page.
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#2 Re: What are Amicable numbers ?

Unread post by scole of TSBT » Sun Jan 29, 2017 12:57 am

I have no issues with Amicable numbers...
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#3 Re: What are Amicable numbers ?

Unread post by Alez » Sun Jan 29, 2017 2:38 am

scole250 wrote:I have no issues with Amicable numbers...
Me neither, seem a friendly bunch on the whole :D

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