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Pseudorandom properties of prime factors

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Abstract

In this paper we study some pseudo-random properties related to the prime factors of integers. We prove some results concerning the well distribution of the greatest prime factor modulo 4, and give some computational insight on the correlations, which seem to be beyond reach of proof.

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References

  1. N. G. De Bruijn, On the number of positive integers ⩽ x, and free prime factors > y.ii, Nederl. Akad. Wetensch. Proc. Ser. A 69, Indag. Math. 28 (1966), 239–247.

    Google Scholar 

  2. Julien Cassaigne, SÉbastien Ferenczi, Christian Mauduit, JoËl Rivat and AndrÁs SÁrkÖzy, On finite pseudorandom binary sequences III (The Liouville function I), Acta Arithmetica 87, no.4 (1999), 367–390.

    Google Scholar 

  3. Julien Cassaigne, SÈbastien Ferenczi, Christian Mauduit, JoËl Rivat and AndrÁs SÁrkÖzy, On finite pseudorandom binary sequences IV (The Liouville function II), Acta Arithmetica 95, no.4 (2000), 343–359.

    Google Scholar 

  4. H. Davenport, Multiplicative number theory (revised by H. L. Montgomery), Springer Verlag, New York, 1980.

    Google Scholar 

  5. GÉrald Tenenbaum and Etienne Fouvry, Entiers sans grand facteur premier en progressions arithmétiques, Proc. London Math. Soc. 63, no.3 (1991), 449–494.

    Google Scholar 

  6. Christian Mauduit, JoËl Rivat and AndrÁs SÁrkÖzy, On the pseudorandom properties of n c, Illinois Journal of Mathematics 46 (2002), 185–197.

    Google Scholar 

  7. Christian Mauduit and AndrÁs SÁrkÖzy, On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol, Acta Arithmetica 82 (1997), 365–377.

    Google Scholar 

  8. Christian Mauduit and AndrÁs SÁrkÖzy, On finite pseudorandom binary sequences, V: On (nα) and (n 2α) sequences, Monatsh. Math. 129 (2000), 197–216.

    Google Scholar 

  9. Christian Mauduit and AndrÁs SÁrkÖzy, On finite pseudorandom binary sequences, VI: On (n kα) sequences, Monatsh. Math. 130 (2000), 281–298.

    Google Scholar 

  10. JoËl Rivat, On pseudo-random properties of P(n) and (n + 1), Periodica Mathematica Hungarica 43 (2001), 121–136.

    Google Scholar 

  11. Michael Rubinstein and Peter Sarnak, Chebyshev’s bias, Experimental Mathematics 3, no.3 (1994), 173–197.

    Google Scholar 

  12. GÉrald Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Société mathématique de France, 1995.

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Oon, SM. Pseudorandom properties of prime factors. Period Math Hung 49, 107–118 (2004). https://doi.org/10.1007/s10998-004-0526-7

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  • DOI: https://doi.org/10.1007/s10998-004-0526-7

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