Let σ_0(n) and σ_1(n) denote the number and sum of the divisors of n, respectively (i.e., the zeroth- and first-order divisor functions). A number n is called sublime if σ_0(n) and σ_1(n) are both perfect numbers. The only two known sublime numbers are 12 and 60865556702383789896703717342431696... ...22657830773351885970528324860512791691264 (Math Pages). It is not known if any odd sublime number exists.

divisor function | perfect number