AMICABLE NUMBERS

Two different numbers are such that the sum of proper divisors of each is equal to the other number.

  •  Proper divisors of a given number are the numbers ( except the number itself ) that can divide the given  number
    Example: Proper divisors of 8 are 1, 2, 4. 


The smallest pair of the amicable number is ( 220, 284 )
  • Proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110
    and the sum of the divisors are 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 +  44 + 55 + 110 = 284.
  • Proper divisors of 284 are 1, 2, 4, 71, 142
    and the sum of the divisors are 1 + 2 + 4 + 71 + 142 = 220.
Other examples include ( 1184, 1210 ), ( 2620, 2924 ), ( 5020, 5564 ), ( 6232, 6368 ), ( 10744, 10856 ), ( 12285, 14595 ) etc.

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