In number theory, a sublime number is a positive integer that has a number of positive divisors (including it) that is a perfect number, and that the sum of these divisors adds another perfect number.

The number 12, for example, is a sublime number. It has a perfect number of positive divisors (6): 1, 2, 3, 4, 6, and 12, and the sum of these is also perfect: 1 + 2 + 3 + 4 + 6 + 12 = 28. There are only two known sublime numbers, 12 and (2) (2 - 1) (2 - 1) (2 - 1) (2 - 1) (2 - 1) (2 - 1) The second of these has 76 decimal digits: 6086555670238378989670371734243169622657830773351885970528324860512791691264.

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