1 . 莫比乌斯函数,由德国数学家和天文学家莫比乌斯提出,数学家梅滕斯首先使用
作为莫比乌斯函数的记号,其在数论中有着广泛应用.所有大于1的正整数
都可以被唯一表示为有限个质数的乘积形式:
(
为
的质因数个数,
为质数,
,
),例如:
,对应
,
,
,
,
,
,
.现对任意
,定义莫比乌斯函数
.
(1)求
,
;
(2)已知
,记
(
为
的质因数个数,
为质数,
,
)的所有因数从小到大依次为
,
,…,
.
(ⅰ)证明:
;
(ⅱ)求
的值(用
(
)表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd9331f692f5f83a74bdba620efe256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e046acc0e785892df1ef03a440b0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5c607987b73502db63f77c9799f4bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d94cf780bb9bf7c7da923a99bac6ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33986442b983a01364b1498d044bbdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/101edd0628caa05cac88bb6f43788ba6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367e788c32187ae2cc97aaa24da1d40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d45fcbbbc2c58f3aaa95a484df08a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf9b1f58f95b13bfe77087ed48038a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75cb6c5e6aeca82ba4ab44c352614c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ad4926e8bf2b42d8a2c568f80c1987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997067e12aa5e1d9b00bb6a9299cb801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf3fff8545c74ca66cd1894a55f7bf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f39b40e3a5a89d2680d1d47a6bb8e3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/142df6665826f73a2706e94be482e066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c16d9bc96f0d4c8992314b315efea8a.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e468312d09c6563c9094b710a35a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e046acc0e785892df1ef03a440b0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5c607987b73502db63f77c9799f4bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d94cf780bb9bf7c7da923a99bac6ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33986442b983a01364b1498d044bbdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
(ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fa827be71e5fc3cad1b94212d9ed0a6.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2453fe8eda2466eaf30ce777d60f07b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c709117ab1d3ef620883a732aed68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33986442b983a01364b1498d044bbdf.png)
您最近一年使用:0次
2 . 古希腊著名的约瑟夫环问题讲的是:共有127个士兵,围成一个环,从一号位的士兵开始,每个存活下来的人依次杀死相邻的下一位士兵,若一名叫做约瑟夫的士兵想要存活到最后,那么他最开始应当站在几号位上?( )
A.1 | B.63 | C.127 | D.31 |
您最近一年使用:0次