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I will give the following
$$\sum_{p\leq x}\frac{1}{p^s} \approx \frac{x^{1-s}}{\log x}$$$$\sum_{p\leq x}\frac{1}{p^s} \approx \frac{1}{1-s}\frac{x^{1-s}}{\log x}$$
for $0\leq s < 1$ and
$$\sum_{p\leq x}\frac{1}{p} \approx \log \log x$$
for $s = 1$.
I will give the following
$$\sum_{p\leq x}\frac{1}{p^s} \approx \frac{x^{1-s}}{\log x}$$
for $0\leq s < 1$ and
$$\sum_{p\leq x}\frac{1}{p} \approx \log \log x$$
for $s = 1$.
I will give the following
$$\sum_{p\leq x}\frac{1}{p^s} \approx \frac{1}{1-s}\frac{x^{1-s}}{\log x}$$
for $0\leq s < 1$ and
$$\sum_{p\leq x}\frac{1}{p} \approx \log \log x$$
for $s = 1$.
I will give the following
$$\sum_{p\leq x}\frac{1}{p^s} \approx \frac{x^{1-s}}{\log x}$$
for $0\leq s < 1$ and
$$\sum_{p\leq x}\frac{1}{p} \approx \log \log x$$
for $s = 1$.
