How to convert difficulty from `mining.set_difficulty` message for Litecoin?

I’m trying to determine how to properly convert difficulty from a mining.set_difficulty message to target for Litecoin, similar to how it’s done for Bitcoin.

For Bitcoin, the process I use is as follows:

I start with the genesis nbits value: 0x1d00ffff

I convert this to the max target:

0x00000000ffff0000000000000000000000000000000000000000000000000000

Then, I calculate the target using this formula:

target = max_target / difficulty

For example, with a difficulty of 524288, the target becomes:

target = max_target / 524288 = 0x0000000000001fffe00000000000000000000000000000000000000000000000

Now, I’m trying to apply a similar algorithm to Litecoin. Here’s what I have so far:

The genesis nbits for Litecoin is 0x1e0ffff0

I convert this to the same max target as in Bitcoin:

0x00000000ffff0000000000000000000000000000000000000000000000000000

I use the formula max_target / 524288, which results in the same target as in Bitcoin:
```
target = 0x0000000000001fffe00000000000000000000000000000000000000000000000
```

However, when I perform this calculation and compare it with the shares I receive on the pool side, I find that some shares have a higher target, such as:

0x0000000005713013fcbf8bf0dcc329a5f56b856c2dbe64603e34b47169eaaa50

Upon further investigation, I found this code snippet, which introduces a coefficient of 65535:

if (opt_algo == ALGO_SCRYPT)
    diff_to_target(work->target, sctx->job.diff / 65536.0);
else
    diff_to_target(work->target, sctx->job.diff);

This suggests that the target for Litecoin should be multiplied by 65535. My question is:

Should the target be scaled by 65535 in the same way?
Why is this adjustment necessary for Scrypt (Litecoin) but not for Bitcoin?
How do I correctly calculate the target for Litecoin to avoid getting shares higher than the calculated target?

Any guidance on this would be appreciated!