To an approximation, the total energy that comes out of a star, what we call luminosity, is constant over a long period of time. If you discount dissipation, over a distance r from the star, this total energy is evenly spread over the sphere of radius r with the star at its center. So, the flux of energy at a distance r from the star is proportional to the inverse squared distance from the star:
flux = L / 4πr²
Where L is the star's luminosity and r is the distance from the star. By the Stephan-Boltzmann law, this flux should be proportional to the fourth power of the temperature of the electromagnetic field in this region. So the fourth power of the temperature in this region should be inversely proportional to the squared distance:
T⁴ ~ L / 4πσr²
r ~ √(L / 4πσ) / T²
Where σ is the Stephan-Boltzmann constant. If you consider the habitable zone to be the region between two temperatures, T0 and T1, thus you would have that the size of this region (R1 - R0) is proportional to √L. So, both the size of this region and how far it is from the star grows with the square root of the star's luminosity. For star's in the main sequence, luminosity is approximately proportional to a power of their mass:
L ~ M3.5
So both the size of the habitable zone and it's distance from a main sequence star is approximately proportional to M1.57. So, you might have a bigger habitable zone in a bigger star, but it would be farther away from the star. In the solar system, and notice that this is the only star system we know well, so any extrapolations we get here might be completely wrong, "planet density" gets much lower when you go farther from the Sun.
In the case of the Sun, the habitable zone is considered to be more or less from 0.5 a.u. to 3.0 a.u., so we have two or three planets in this range. Sirius have about twice this mass, so it's habitable zone should from about 1.5 a.u. to about 9 a.u..
How many planets could you have in such a region? Well... who knows? The sun have just two planets within this range (mars and jupiter), but that means little. The key here would be "how many planets can I put there and it would still be stable". That's very difficult to know.
But let's risk it anyway, and be clear that from this line below I'm speculating WILDLY. Let's say that for a planet to be stable, the influence of the gravity of its neighbors as a fraction of the gravitational influence of the star should be no bigger than the influence of Jupiter in the Earth. The gravitational pull of the Sun over the Earth is about 20 thousand times bigger than the gravitational pull of Jupiter.
So, let's say we want to know how many earth sized planets you could put around Sirius in circular orbits between 1.5 a.u. and 9 a.u. so that the gravitational pull between them is 20 thousandths