Given two positive numbers N and M, the task is to check whether the given pairs of numbers (N, M) form a Betrothed Numbers or not.
Input: N = 48, M = 75
The proper divisors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24
Sum of proper divisors of 48 is 75(sum1)
The proper divisors of 75 are 1, 3, 5, 15, 25
Sum of proper divisors of 48 is 49(sum2)
Since sum2 = N + 1, therefore the given pairs form berothered numbers.
Input: N = 95, M = 55
The proper divisors of 95 are 1, 5, 19
Sum of proper divisors of 48 is 25(sum1)
The proper divisors of 55 are 1, 5, 11
Sum of proper divisors of 48 is 17(sum2)
Since Neither sum2 is equals N + 1 nor sum1 is equals to M + 1, therefore the given pairs doesn’t form berothered numbers.
- Find the sum of proper divisors of the given numbers N and M.
- If sum of proper divisors of N is equals to M + 1 or sum of proper divisors of M is equals to N + 1 then the given pairs form a Betrothed Numbers.
- Else it doen’t forms a pair of Betrothed Numbers.
Below is the implementation of the above approach:
Time Complexity: O(√N + √M)
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- Betrothed numbers
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