Well, let's assume for a second that psychics exist and know that they are psychic. The second assumption is kind of important as if they just act on impulse without knowing they're psychic we can't really differentiate that from all the other chance winnings on a hunch.

For the Powerball, two ways to play: pick your own numbers or randomly generate them. Would a winning psychic choose one over the other more often? An ability to sense and know the future means they would have to either know the winning numbers and pick them, know the machine that produces the numbers (but not necessarily the numbers themselves), or somehow manipulate chance or psychics so that the lottery machine produces the psychic's number during the draw.

Psychic is kind of loosely defined right now by your question so for convenience let's rule out the last one since that's more telekinetic/magic than psychic.

With these conditions, we should see some pattern from the winner: they would either always pick their own and get the winning numbers or they would always happen to go to the right machine at the right time.

Both should show pretty consistent behavior on the part of a psychic, as we can see that the bar for big winnings is pretty low ($600) and multiple statistically improbable winnings would likely be investigated. (per the atriclr, only 10 states do not investigate frequent winners).

So to summarize so far:

Frequent winners very likely investigated unless they are in the 10 states

Psychic will likely pick their own numbers

Psychic will go to a specific machine and have erratic pattern of purchase

If psychic are playing the lottery, my assumptions lead me to think that it makes no sense to frequently win, instead banking on a single explainable big win. This of course would be only if the psychic did not want to be found out as a psychic, which for the purpose of the lottery I think would be a valid want as I believe that there are rules about additional knowledge, etc meant to catch people defrauding the lottery. Future-visions would most definitely qualify, so probably would require that the psychic forfeit their winnings.

The mundane explanations do explain a lot, both from the investigations and admissions from the frequent winners. To me anyways, the psychics, if they exist, would more likely be the one time big winners, not the frequent ones.