托词和共转词

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从1到的整数${\显示样式\脚本样式n}$那是互质到${\显示样式\脚本样式n}$被称为总计属于${\显示样式\脚本样式n}$，而从1到的其余整数${\显示样式\脚本样式n}$被称为共转.

欧拉函数是的总数${\显示样式\脚本样式n}$，同时欧拉共音函数是的共转数${\显示样式\脚本样式n}$.

托塔提斯

的一组总计${\显示样式\脚本样式n}$是（请参见共素三角形)

${\显示样式\{1\leqi\leqn~|~（n，i）=1\}，}$

哪里${\显示样式\脚本样式（n，i）}$是最大公约数（GCD）第页，共页${\显示样式\脚本样式n}$和$｛\displaystyle\scriptstyle i｝$

因此，欧拉函数是基数的一组总计${\显示样式\脚本样式n}$:

${\displaystyle\varphi（n）：=|\{1\leqi\leqn~|~（n，i）=1\}|.}$

（请注意，在下表中，列出的大多数序列都是无限的，因此我们指的是该序列中所有小于${\显示样式n}$).

总计表

${\显示样式\脚本样式n}$	的图腾${\显示样式\脚本样式n}$	A编号	的Totient${\显示样式\脚本样式n}$ A000010美元
1	{1}		1
2	{1}		1
三	{1, 2}		2
4	{1, 3}		2
5	{1, 2, 3, 4}		4
6	{1, 5}		2
7	{1, 2, 3, 4, 5, 6}		6
8	{1, 3, 5, 7}		4
9	{1, 2, 4, 5, 7, 8}	A001651号	6
10	{1, 3, 7, 9}		4
11	{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}		10
12	{1, 5, 7, 11}		4
13	{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}		12
14	{1, 3, 5, 9, 11, 13}		6
15	{1, 2, 4, 7, 8, 11, 13, 14}		8
16	{1, 3, 5, 7, 9, 11, 13, 15}		8
17	{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}		16
18	{1, 5, 7, 11, 13, 17}		6
19	{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18}		18
20	{1, 3, 7, 9, 11, 13, 17, 19}		8
21	{1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19, 20}		12
22	{1, 3, 5, 7, 9, 13, 15, 17, 19, 21}		10
23	{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22}		22
24	{1, 5, 7, 11, 13, 17, 19, 23}		8
25	{1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24}		20
26	{1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25}		12
27	{1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26}	A001651号	18
28	{1, 3, 5, 9, 11, 13, 15, 17, 19, 23, 25, 27}		12
29	{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28}		28
30	{1, 7, 11, 13, 17, 19, 23, 29}		8

累加产生有限序列的无限序列

{{1}, {1}, {1, 2}, {1, 3}, {1, 2, 3, 4}, {1, 5}, {1, 2, 3, 4, 5, 6}, {1, 3, 5, 7}, {1, 2, 4, 5, 7, 8}, {1, 3, 7, 9}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, {1, 5, 7, 11}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, {1, 3, 5, 9, 11, 13}, ...}

其串联给出：

A038566号规范中的分子双射从正整数到正理性<=1：按递增方式排列分数分母然后通过增加分子.

{1, 1, 1, 2, 1, 3, 1, 2, 3, 4, 1, 5, 1, 2, 3, 4, 5, 6, 1, 3, 5, 7, 1, 2, 4, 5, 7, 8, 1, 3, 7, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 5, 7, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 3, 5, 9, 11, 13, ...}

A000010美元 欧拉函数 ${\displaystyle\scriptstyle\varphi（n），\ n\，\geq\，1，}$（数到${\显示样式\脚本样式n}$和互质${\显示样式\脚本样式n}$).

{1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 8, 8, 16, 6, 18, 8, 12, 10, 22, 8, 20, 12, 18, 12, 28, 8, 30, 16, 20, 16, 24, 12, 36, 18, 24, 16, 40, 12, 42, 20, 24, 22, 46, 16, 42, 20, 32, 24, 52, 18, 40, 24, 36, 28, ...}

的所有目标${\显示样式\脚本样式n\，\geq\，3}$是平的，因为$｛\displaystyle\scriptstyle k｝$是totative当且仅当$｛\displaystyle\scriptstylen-k｝$是totative，而${\displaystyle\scriptstyle{\frac{n}{2}}}$显然不能是的总和${\显示样式\脚本样式n}$.

分离的totalities

一个孤立的婴儿，${\显示样式\脚本样式k}$第，页，共页${\显示样式\脚本样式n}$是小于和的正整数互质到${\显示样式\脚本样式n}$如此一来${\显示样式\脚本样式k-1}$也不是${\显示样式\脚本样式k+1}$是互质的${\显示样式\脚本样式n}$.

A132952号 ${\显示样式\脚本样式a（n）}$=的孤立总数${\显示样式\脚本样式n}$.

{0, 1, 0, 2, 0, 2, 0, 4, 0, 4, 0, 4, 0, 6, 2, 8, 0, 6, 0, 8, 2, 10, 0, 8, 0, 12, 0, 12, 0, 8, 0, 16, 2, 16, 2, 12, 0, 18, 2, 16, 0, 12, 0, 20, 6, 22, 0, 16, 0, 20, 2, 24, 0, ...}

A132953号 ${\显示样式\脚本样式a（n）}$=${\显示样式\脚本样式n}$.

{0, 1, 0, 4, 0, 6, 0, 16, 0, 20, 0, 24, 0, 42, 15, 64, 0, 54, 0, 80, 21, 110, 0, 96, 0, 156, 0, 168, 0, 120, 0, 256, 33, 272, 35, 216, 0, 342, 39, 320, 0, 252, 0, 440, 135, ...}

共同名词

共转数的集合${\显示样式\脚本样式n}$是（请参见共素三角形)

$显示样式$

哪里${\显示样式\脚本样式（n，i）}$是最大公约数（GCD）第页，共页${\显示样式\脚本样式n}$和$｛\displaystyle\scriptstyle i｝$

因此，欧拉共音函数是基数关于${\显示样式\脚本样式n}$:

${\显示样式{\上划线{\varphi}}（n）：=|\{1\leqi\leqn~|~（n，i）>1\}|.}$

另请参见

• 雅各布斯塔尔函数