An Extension of Heilbronn's Class-Number Theorem

Let h(d) denote the number of primitive classes of binary quadratic forms of negative discriminant d. Heilbronn has recently proved that

Theorem I.

h(d)→∞

as -d→∞.

By a slight modification of Heilbronn's argument I show that

Theorem II.

h(d)/2^t→∞

as -d→∞,

where t is the number of different prime factors of d.