On exponentially coprime integers

Details On exponentially coprime integers On exponentially coprime integers

2006-10-09

arxiv.org/abs/math/0610275v1

Pure Math. Appl. (PU.M.A.), 15 (2004), 343-348

Mathematics

Number Theory

Scientific paper

The integers $n=\prod_{i=1}^r p_i^{a_i}$ and $m=\prod_{i=1}^r p_i^{b_i}$ having the same prime factors are called exponentially coprime if $(a_i,b_i)=1$ for every $1\le i\le r$. We estimate the number of pairs of exponentially coprime integers $n,m\le x$ having the prime factors $p_1,...,p_r$ and show that the asymptotic density of pairs of exponentially coprime integers having $r$ fixed prime divisors is $(\zeta(2))^{-r}$.

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