table of values of the Möbius function and the Mertens function

The following table lists the values of the Möbius function $\mu (n)$ and the Mertens function $M(n)$ for . The Möbius function is defined as $\mu (n)={(-1)}^{\omega (n)}$ (where $\omega (n)$ is the number of distinct prime factors function) for squarefree numbers, and $\mu (n)=0$ for any integer with a repeated prime factor. The Mertens function is the matching summatory function for the Möbius function,

$$M(n)=\sum _{i=1}^n\mu (i).$$

$n$	$\mu (n)$	$M(n)$	$n$	$\mu (n)$	$M(n)$	$n$	$\mu (n)$	$M(n)$	$n$	$\mu (n)$	$M(n)$
1	1	1	26	1	$-1$	51	1	$-2$	76	0	$-3$
2	$-1$	0	27	0	$-1$	52	0	$-2$	77	1	$-2$
3	$-1$	$-1$	28	0	$-1$	53	$-1$	$-3$	78	$-1$	$-3$
4	0	$-1$	29	$-1$	$-2$	54	0	$-3$	79	$-1$	$-4$
5	$-1$	$-2$	30	$-1$	$-3$	55	1	$-2$	80	0	$-4$
6	1	$-1$	31	$-1$	$-4$	56	0	$-2$	81	0	$-4$
7	$-1$	$-2$	32	0	$-4$	57	1	$-1$	82	1	$-3$
8	0	$-2$	33	1	$-3$	58	1	0	83	$-1$	$-4$
9	0	$-2$	34	1	$-2$	59	$-1$	$-1$	84	0	$-4$
10	1	$-1$	35	1	$-1$	60	0	$-1$	85	1	$-3$
11	$-1$	$-2$	36	0	$-1$	61	$-1$	$-2$	86	1	$-2$
12	0	$-2$	37	$-1$	$-2$	62	1	$-1$	87	1	$-1$
13	$-1$	$-3$	38	1	$-1$	63	0	$-1$	88	0	$-1$
14	1	$-2$	39	1	0	64	0	$-1$	89	$-1$	$-2$
15	1	$-1$	40	0	0	65	1	0	90	0	$-2$
16	0	$-1$	41	$-1$	$-1$	66	$-1$	$-1$	91	1	$-1$
17	$-1$	$-2$	42	$-1$	$-2$	67	$-1$	$-2$	92	0	$-1$
18	0	$-2$	43	$-1$	$-3$	68	0	$-2$	93	1	0
19	$-1$	$-3$	44	0	$-3$	69	1	$-1$	94	1	1
20	0	$-3$	45	0	$-3$	70	$-1$	$-2$	95	1	2
21	1	$-2$	46	1	$-2$	71	$-1$	$-3$	96	0	2
22	1	$-1$	47	$-1$	$-3$	72	0	$-3$	97	$-1$	1
23	$-1$	$-2$	48	0	$-3$	73	$-1$	$-4$	98	0	1
24	0	$-2$	49	0	$-3$	74	1	$-3$	99	0	1
25	0	$-2$	50	0	$-3$	75	0	$-3$	100	0	1

Title	table of values of the Möbius function and the Mertens function
Canonical name	TableOfValuesOfTheMobiusFunctionAndTheMertensFunction
Date of creation	2013-03-22 18:06:27
Last modified on	2013-03-22 18:06:27
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	5
Author	PrimeFan (13766)
Entry type	Data Structure
Classification	msc 11A25