# 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 $0. 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 TableOfValuesOfTheMobiusFunctionAndTheMertensFunction 2013-03-22 18:06:27 2013-03-22 18:06:27 PrimeFan (13766) PrimeFan (13766) 5 PrimeFan (13766) Data Structure msc 11A25