on some occasions

[color=indigo]1-On some occasions when he looked tired, I let him take a break.
[color=red]2-On some of the occasions when he looked tired, I let him take a break.

Do these sentences have the exact same meaning?
Do both imply that there were occasions when he did not look tired and I did not let him take a break?

Gratefully,
Navi.

The meaning is the same. They could indicate that there were occasions when he DID look tired but I did not let him take a break, and this inference seems to be stronger in the second sentence than the first one.