Permutations: a(k) Coprime To k

[Leroy Quet]

What is the number of permutations, {a(1),a(2),a(3),...,a(m)}, of
{1,2,3,...,m} where each a(k) is relatively prime to each k, for 1 <=
k <= m?

Is there an easy way to calculate this counting-sequence directly?

Thanks,
Leroy Quet