I am looking for the pure math answer here, no other poker elements involved.

If there is $5 in the pot, Player A bets $5 and Players B calls $5. I am getting 3-1 on my money. How many outs do I need to make the mathematically correct play?

Now 4-1 on my money, how many outs?
Now 5-1 on my money, how many outs?

Tom

The number of 13 outs for 2-1 on your money (i.e. call a potsized bet HU) is actually a bit on the low side; most of times it is a good heuristics but it presupposes a bit of implied odds.

Assuming this is PLO hi, that we are on the turn (45 cards unseen), and there are no implied odds:

for 2 to 1 pot odds: 15 clean outs
for 3 to 1 pot odds: about 11 outs
for 4 to 1 pot odds: 9 outs

for n to 1 pot odds: 45/(n+1) outs.

So in general you divide 45 by the number of players in the hand (including yourself).

Corollary: if everyone would move in on the turn you could call with only a gutshot...

Of course you know that you almost always have to factor in other aspects. One that wasn't mentioned before is that if you consider taking one off on the flop, then even if you make your hand on the turn river you may get counterfeited on the river. For this, use the killer card chart in SS2.