Two numbers are said to be betrothed if the sum of the proper divisors of each number is 1 more than the value of the other. For example:

The proper divisors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, and 24. 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 = 76 = 75 + 1.

The proper divisors of 75 are 1, 3, 5, 15, and 25. 1 + 3 + 5 + 15 + 25 = 49 = 48 + 1.

Interestingly, in all such pairs discovered so far, one number is odd and the other even. Is this always the case? That’s an open question.