Sublime number

Sublime number

In mathematics, a sublime number is a positive integer which has a perfect number of positive divisors (including itself), and whose positive divisors add up to another perfect number. [MathPages article, [http://www.mathpages.com/home/kmath202/kmath202.htm "Sublime Numbers"] .]

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 again a perfect number: 1 + 2 + 3 + 4 + 6 + 12 = 28.

There are only two known sublime numbers, 12 and (2126)(261 − 1)(231 − 1)(219 − 1)(27 − 1)(25 − 1)(23 − 1) OEIS|id=A081357. [Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning" New York: Oxford University Press (2003): 215] The second of these has 76 decimal digits::6086555670238378 989670371734243169622657830773 351885970528324860512791691264.

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