Amicable Number

The two digits of the number of A and B will be friendly to each other if

sum of all proper manufacturers of  A  and sum of all proper 

manufacturers  of B  are  equal. So thus two digits are called 

Amicable Number.

Such as 220 and 282 are Amicable Number . Because

The manufacturers of 220 are 1,2,4,5,10,11,21,44,53 and 110.

The sum of manufacture is (1+2+4+5+10+11+21+44+53=282).

Besides the  manufacturers of 282 are 1,2,4,71 and 142.

 The sum of manufactures of (1+2+4+71+142=240).

so 220 and 282 ar friendly to each other .

Ten amicable number are (1184,1210),(2620,2924),(5020,5564),

(6232,6368),(10744,10856),(12285,14595),(17296,18416),

(63020,76084).

Amicable Number pair was discovered by the Pythagoreans .

A few interesting characters :

1.  No amicable number thats one of two numbers is a square.
   
2. Some amicable number (x,y) in which the sum of digits of x and y is equal . Such as (100485,124155)
   100485=1+0+0+4+8+5=18124155=1+2+4+1+5+5=18