Singular integer right triangles

It turns out that $12$ cm is the smallest length of wire that can be bent to form an integer sided right angle triangle in exactly one way, but there are many more examples.

$12$ cm: ($3$,$4$,$5$) $24$ cm: ($6$,$8$,$10$) $30$ cm: ($5$,$12$,$13$) $36$ cm: ($9$,$12$,$15$) $40$ cm: ($8$,$15$,$17$) $48$ cm: ($12$,$16$,$20$)

In contrast, some lengths of wire, like $20$ cm, cannot be bent to form an integer sided right angle triangle, and other lengths allow more than one solution to be found; for example, using $120$ cm it is possible to form exactly three different integer sided right angle triangles.

$120$ cm: ($30$,$40$,$50$), ($20$,$48$,$52$), ($24$,$45$,$51$)

Given that L is the length of the wire, for how many values of $L ≤ 1,500,000$ can exactly one integer sided right angle triangle be formed?