Humble Number

Relevant wiki: Perfect Numbers

ATTENTION! This is complicated and I hope you pay attention closely.

So, the next term is derived by multiplying the next even perfect number by the next prime number and adding the previous term. $eg. 6 \times 2 + 1 = 13$ where $6$ is the $1^{st}$ even perfect number and $2$ is the $1^{st}$ prime number and where $1$ is the previous term.

According to the formula (for deriving even perfect numbers), If $2^p -1$ is prime then $(2^p-1)(2^{p-1})$ is (an even) perfect. So applying this formula, the next even perfect numbers are $28, 496, 8128, 33550336$ . (We are stopping at 33550336 for the purpose of this question if not the numbers get crazy big and I mean it: $\huge crazy$ )

Allow me to demonstrate the numbers in the question:

$97 = 28 \times 3 + 13$

$2577 = 496 \times 5 + 97$

$59473 = 8128 \times 7 + 2577$

So, the next number should be $33550336 \times 11 + 59473 = 369113169$

$\large \text {P.S. Notice that 3,6,9 contains multiples of 3 and 169 is the square of 13 which is the number before it.}$