Numbers equal to Sum of Primes not Greater than its Prime Counting Function Value

Theorem
Let $\map \pi n: \Z_{\ge 0} \to \Z_{\ge 0}$ denote the prime-counting function:
 * $\map \pi n =$ the count of the primes less than $n$

Consider the equation:
 * $\ds n = \sum_{p \mathop \le \map \pi n} p$

where $p \le \pi \left({n}\right)$ denotes the primes not greater than $\pi \left({n}\right)$.

Then $n$ is one of:
 * $5, 17, 41, 77, 100$

Proof
We have that: