While analysing the average runtime of an algorithm, I came across the following identity, and would like to know if anybody knows of any references for it? 


For $i \in \mathbb{N}$, let $\bar{s}(i)$ denote the square-free part of $i$, eg., $\bar{s}(12) = 3$ (and $\bar{s}(1)=1$). Then
$$
\lim\_{n \rightarrow \infty} \frac{\sum\_{i=1}^{n} \bar{s}(i)}{n^2} = \frac{\pi^2}{30}.
$$


Many thanks.



Reference requested for $\lim_{n \rightarrow \infty} \frac{\sum_{i=1}^{n} \bar{s}(i)}{n^2} = \frac{\pi^2}{30}$
The question asked for a reference, not a proof. A reference is Karl Greger, Square divisors and square-free numbers, Mathematics Magazine 51, No. 4 (Sept. 1978), 211-219. I make no claim that the result was unknown before Greger's paper. 


