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In number theory, the Erdős arcsine law, named after Paul Erdős in 1969, states that the prime divisors of a number have a distribution related to the arcsine distribution. Specifically, say that the jth prime factor p of a given number n (in the sorted sequence of distinct prime factors) is "small" when log log p < j.Then, for any fixed parameter u, in the limit as x goes to infinity, the proportion of the integers n less than x that have fewer than u log log n small prime factors converges to

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  • Llei de l'arcsinus d'Erdős (ca)
  • Erdős arcsine law (en)
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  • En teoria de nombres, la llei de l'arcsinus d'Erdős, que duu el nom de Paul Erdős, afirma que els divisors primers d'un nombre segueixen una distribució relacionada amb la distribució arcsinus. En particular, diu que el factor primer j-èssim p d'un nombre donat n (en la seqüència ordenada dels diferents factors primers) és "petit" quan log log p < j. Llavors, per qualsevol valor fix del paràmetre u, en el límit quan x tendeix a infinit, la proporció d'enters n menors que x que tenen menys que u log log n factors primers petits convergeix a: (ca)
  • In number theory, the Erdős arcsine law, named after Paul Erdős in 1969, states that the prime divisors of a number have a distribution related to the arcsine distribution. Specifically, say that the jth prime factor p of a given number n (in the sorted sequence of distinct prime factors) is "small" when log log p < j.Then, for any fixed parameter u, in the limit as x goes to infinity, the proportion of the integers n less than x that have fewer than u log log n small prime factors converges to (en)
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  • En teoria de nombres, la llei de l'arcsinus d'Erdős, que duu el nom de Paul Erdős, afirma que els divisors primers d'un nombre segueixen una distribució relacionada amb la distribució arcsinus. En particular, diu que el factor primer j-èssim p d'un nombre donat n (en la seqüència ordenada dels diferents factors primers) és "petit" quan log log p < j. Llavors, per qualsevol valor fix del paràmetre u, en el límit quan x tendeix a infinit, la proporció d'enters n menors que x que tenen menys que u log log n factors primers petits convergeix a: (ca)
  • In number theory, the Erdős arcsine law, named after Paul Erdős in 1969, states that the prime divisors of a number have a distribution related to the arcsine distribution. Specifically, say that the jth prime factor p of a given number n (in the sorted sequence of distinct prime factors) is "small" when log log p < j.Then, for any fixed parameter u, in the limit as x goes to infinity, the proportion of the integers n less than x that have fewer than u log log n small prime factors converges to (en)
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