Amicable Pairs Coding Challenge | Dataford Interview Questions

Your question is Amicable Pairs Coding Challenge. Start with the requirements on the right.

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Problem

Dynata data-quality checks may need to classify mathematical relationships between numeric values. Given two positive integers, determine whether they form an amicable pair.

Two distinct numbers a and b are amicable when the sum of the proper divisors of a equals b, and the sum of the proper divisors of b equals a. A proper divisor is a positive divisor smaller than the number itself.

Your solution must avoid scanning every integer from 1 through n. Use divisor-pair reasoning so that each number can be processed in O(sqrt(n)) time.

Formal Specification

Implement amicable_pair(a, b).

Input: Two positive integers a and b.
Output: Return True if they form an amicable pair, otherwise return False.
The numbers must be distinct. A perfect number paired with itself is not considered an amicable pair.

Constraints

1 <= a, b <= 10^12
a and b are positive integers
The inputs must be distinct for the result to be True
Do not scan every integer from 1 through either input

Function Signature

def amicable_pair(a, b):