Sublime Number

Let $\tau(n)$ and $\sigma(n)$ 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 $\tau(N)$ and $\sigma(N)$ are both Perfect Numbers. The only two known sublime numbers are 12 and

$60865556702383789896703717342431696\cdots$
$\cdots 22657830773351885970528324860512791691264.$

It is not known if any Odd sublime number exists.

See also Divisor Function, Perfect Number