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

它也等于这些自然数的调和平均值的倒数的倍。它可以推广到正整数的倒数的幂之和，即。

根据定义，调和数满足递推关系

它也满足恒等式

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 is prime are