I have a reference request related to the result :

$\sum_{n=2}^{x} P(n)$ ~ $\frac{\pi^2}{12}\frac{x^{2}}{log(x)}$ as $x \rightarrow \infty$

where $P(n)$ is the largest prime factor of the positive integer $n$.

Theorem 1.1 in [1] below appears to be the first proof of this result and the result was generalized in Theorem 3.1 in [2] below.

I am looking for upper and lower bounds on the ratio L/R where L and R are the left and right sides respectively of the asymptotic relation above.

Thanks for any help.

References

[1]. K.Alladi and P.Erdos. Pacific J. Math. 71(1977) 275-294

[2]. J.De Konnick and R.Sitaramachandrarao. Indian J. Pure Appl Math. 19(10) 990-1004 Oct 1988

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