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# Uniform O-estimates of certain error functions connected with k-free integers

Published online by Cambridge University Press:  09 April 2009

## Extract

Let k be a fixed integer ≧ 2. A positive integer m is called k-free if m is not divisible by the k'th power of any integer > 1. Let qk(m) be the characteristic function of the set of k-free integers; that is, qk(m) = 1 or 0 according as m is k-free or not. It can be easily shown that where μ(n) is the Mobius function. Let x ≧ 1 denote a real variable and n be a positive integer. Let Qk(x, n) and be the number and the sum of the reciprocals of the k-free integers ≦ x which are prime to n respectively.

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Research Article
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## References

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