An amicable pair (m, n) consists of two integers m, n for which the sum of proper divisors (the divisors excluding the number itself) of one number equals the other. Amicable pairs are occasionally called friendly pairs, although this nomenclature is to be discouraged since the numbers more commonly known as friendly pairs are defined by a different, albeit related, criterion. Symbolically, amicable pairs satisfy s(m) | = | n s(n) | = | m, where s(n) congruent σ(n) - n is the restricted divisor function.

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