at other times

I've noticed that people usually say at other times. However, I've also seen instances of other times, without the preposition at.

When do we use at and when don't we need it when we use other times?

Sometimes the train is on time, (at) other times it's delayed.
Sometimes the train is on time, other times it's delayed.

Sometimes she is kind, other times she's not.
Sometimes she is kind, at other times she's not.
Sometimes she is kind than at other times.
Sometimes she is kind than other times.
Sometimes she is kind, others she's not.

Sometimes the examinations are harder than other times.
Sometimes the examinations are harder, other times easier.

Sometimes its more difficult than [at] other times. Sometimes it is more difficult, other times it is less difficult.
I'm more tired some times than [at] other times. It depends on the day.

Sometimes it takes longer than other times.
Sonetimes it takes 5 minutes, [at] other times it takes longer.

Sometimes the drinks taste better than other times.
Sometimes the juice tastes very good, at other times it taste not so good.

regards