Inclusion-exclusion formula for the Liouville Lambda function.

Question

The Riemann hypothesis is equivalent to: $$\lim_{n\to \infty } \, \frac{\sum\limits_{k=1}^n \lambda (k)}{n^{\frac{1}{2}+\epsilon}}=0$$ according to "The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike" by Peter Borwein, at page 6.
where: $$L(n) = \sum\limits_{k=1}^n \lambda (k)$$ Is the following inclusion-exclusion formula for the partial sums of the Liouville lambda function correct? $$L(n) = \underbrace{\underset {a^2\leq n} {\sum_ {a\geq 1}} 1 - \underset {a^2 b\leq n} {\sum_ {a\geq 1}\sum_ {b\geq 2}} 1 + \underset {a^2 bc\leq n} {\sum_ {a\geq 1}\sum_ {b\geq 2}\sum_ {c\geq 2}} 1 - \underset {a^2 bcd\leq n} {\sum_ {a\geq 1}\sum_ {b\geq 2}\sum_ {c\geq 2}\sum_ {d\geq 2}} 1 + \cdots}_{\text{number of alternating sums} > \frac{\log(n)}{\log(2)}}$$