{
  "id": "math/0610275",
  "version": "v1",
  "published": "2006-10-09T08:27:35.000Z",
  "updated": "2006-10-09T08:27:35.000Z",
  "title": "On exponentially coprime integers",
  "authors": [
    "László Tóth"
  ],
  "journal": "Pure Math. Appl. (PU.M.A.), 15 (2004), 343-348",
  "categories": [
    "math.NT"
  ],
  "abstract": "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 $(\\zeta(2))^{-r}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-09T08:27:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A05",
      "11A25",
      "11N37"
    ],
    "keywords": [
      "exponentially coprime integers",
      "prime factors",
      "asymptotic density",
      "fixed prime divisors"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10275T"
    }
  }
}