What is Solitary Number?

A number is said to be Solitary if it does not have any friendly pair. Example 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 21, ...

A friendly pair is a pair of numbers that has the same ratio of the sum of divisors to the number itself.

For example, 6 and 28 are friendly.
6 has divisors 1,2,3,6; 1+2+3+6 = 12/6 = 2
28 has divisors 1,2,4,7,14,28; 1+2+4+7+14+28 = 56/28 = 2

Solitary Numbers include all prime numbers, all powers of prime numbers, and all other numbers where the ratio of the sum of the divisors to the number itself matches no other ratio.
18, 45, 48, 52, 136, 148, 160, 162, 176, 192, 196, 208, 232, 244, 261, 272, 292, 296, 297, 304, 320, 352, and 369 are all solitary numbers.