Distinct Terms in a Multiplication Table
Let $P(m,n)$ be the number of distinct terms in an $m\times n$ multiplication table.
For example, a $3\times 4$ multiplication table looks like this:
| $\times$ | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 |
| 2 | 2 | 4 | 6 | 8 |
| 3 | 3 | 6 | 9 | 12 |
There are $8$ distinct terms $\{1,2,3,4,6,8,9,12\}$, therefore $P(3,4) = 8$.
You are given that:
$P(64,64) = 1263$,
$P(12,345) = 1998$, and
$P(32,10^{15}) = 13826382602124302$.
Find $P(64,10^{16})$.