A number such that both the sum of its divisors and the number of its divisors are perfect numbers. The smallest sublime number is 12. There are 6 divisors of 12 - 1, 2, 3, 4, 6, and 12 - the sum of which is 28. Both 6 and 28 are perfect. The second sublime number begins 60865..., ends ...91264, and has a total of 76 digits! It is not known if there are larger even sublime numbers, nor if there are any odd sublime numbers.
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