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Amicable Numbers
Definition 1
Two natural numbers
and 
are amicable numbers (an amicable pair or simply amicable) if each is the sum
of the proper divisors
of the other.
and are amicable numbers (an amicable pair or simply amicable) if each is the sum
of the proper divisors
of the other.
Example 1
The smallest amicable pair is 
and 
. Indeed the sum of proper divisors of 
is:
and the sum of proper divisors of 
is:
and . Indeed the sum of proper divisors of is:
is: