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A Note on the Divisor Function dk(n)

MENG Zaizhao   

  1. Department of Mathematics and Institute of Mathematics, Peking University, Beijing, 100871
  • Received:2000-09-12 Online:2001-09-20 Published:2001-09-20

关于除数函数dk(n)的一个注记

蒙在照   

  1. 北京大学数学系、数学研究所,北京,100871

Abstract: Let dk(n) denote the k-fold iterated divisor function(k≥2). It is proved that for sufficiently large x, {dk(n)=dk(n+1), k≥2} hold for ≥x(loglogx)-2.5 integers nx

Key words: divisor function, arithmetic function

摘要: dk(n)为k重除数函数(k≥2)。证明了:对充分大正数x, 同时使等式组{dk(n)=dk(n+1), k≥2}成立且不超过xn的个数为≥x(loglogx)-2.5

关键词: 除数函数, 数论函数

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