调和数

调和数可以指跟约数和有关的整数欧尔调和数。在数学上，第n个调和数是首n个正整数的倒数和，即

$H_n= 1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n} =\sum_{k=1}^n \frac{1}{k}$

它也等于这些自然数的调和平均值的倒数的 $n$ 倍。它可以推广到正整数的倒数的幂之和，即 $H_n^{(m)}=\sum_{k=1}^n \frac{1}{k^m}$ 。

根据定义，调和数满足递推关系

$H_{n+1} = H_{n} + \frac{1}{n+1}$

它也满足恒等式

$\sum_{k=1}^n H_k = (n+1) H_n - n$

单词	Harmonic number
释义	Harmonic number 中文百科调和数调和数可以指跟约数和有关的整数欧尔调和数。在数学上，第n个调和数是首n个正整数的倒数和，即 $H_n= 1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n} =\sum_{k=1}^n \frac{1}{k}$ 它也等于这些自然数的调和平均值的倒数的 $n$ 倍。它可以推广到正整数的倒数的幂之和，即 $H_n^{(m)}=\sum_{k=1}^n \frac{1}{k^m}$ 。根据定义，调和数满足递推关系 $H_{n+1} = H_{n} + \frac{1}{n+1}$ 它也满足恒等式 $\sum_{k=1}^n H_k = (n+1) H_n - n$ 英语百科 Harmonic number 调和数 In mathematics, the n-th harmonic number is the sum of the reciprocals of the first n natural numbers: This also equals n times the inverse of the harmonic mean of these natural numbers. The numbers n such that the numerator of the fully reduced expression for $H_n$ is prime are
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Harmonic number