Sublime Number

Let  and  denote the number and sum of the divisors of , respectively (i.e., the zeroth- and first-order divisor functions). A number  is called sublime if  and  are both perfect numbers. The only two known sublime numbers are 12 and

(Math Pages). It is not known if any odd sublime number exists.

REFERENCES:

MathPages. "Sublime Numbers." https://www.mathpages.com/home/kmath202.htm.