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

Key words: divisor function, arithmetic function

摘要： 设d_k(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{d_k(n)=d_k(n+1), k≥2}成立且不超过x的n的个数为≥x(loglogx)^-2.5。

关键词: 除数函数, 数论函数