Geodesic
Normal numbers and the middle prime factor of an integer
Jean-Marie De Koninck 1   ; Imre Kátai 2
1 Département de mathématiques et de statistique Université Laval Québec, QC G1V 0A6, Canada
2 Computer Algebra Department Eötvös Lorand University Pázmány Péter sétány 1/C 1117 Budapest, Hungary
Colloquium Mathematicum, Tome 135 (2014) no. 1, pp. 69-77 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $p_m(n)$ stand for the middle prime factor of the integer $n\ge 2$. We first establish that the size of $\log p_m(n)$ is close to $\sqrt {\log n}$ for almost all $n$. We then show how one can use the successive values of $p_m(n)$ to generate a normal number in any given base $D\ge 2$. Finally, we study the behavior of exponential sums involving the middle prime factor function.
DOI : 10.4064/cm135-1-5
Keywords: stand middle prime factor integer first establish size log close sqrt log almost successive values generate normal number given base finally study behavior exponential sums involving middle prime factor function

Jean-Marie De Koninck  1   ; Imre Kátai  2

1 Département de mathématiques et de statistique Université Laval Québec, QC G1V 0A6, Canada
2 Computer Algebra Department Eötvös Lorand University Pázmány Péter sétány 1/C 1117 Budapest, Hungary 
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Jean-Marie De Koninck; Imre Kátai. Normal numbers and the middle prime factor
 of an integer. Colloquium Mathematicum, Tome 135 (2014) no. 1, pp. 69-77. doi: 10.4064/cm135-1-5

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