整数,使得十进制表示的非零子序列不能被 n 整除。n=2,3,4,5,6,7,8,9, .......
把某个n相关的一串数(取倒数)加起来,记和为a(n)。
a(n)=3, 5, 8, 11, 14, 18, 21, 25, 29, 33, 37, 41, 45, 49, 54, 58, 62, 67, 71, 76, 81,
85, 90, 95, 100, 105, 109, 114, 119, 124, 129, 134, 140, 145, 150, ..........
求证:\(a(n)=\displaystyle\bigg\lfloor\sum_{k=1}^n\ \frac{n}{k}\bigg\rfloor\)
|