table of values of the Liouville function and its summatory function
TableOfValuesOfTheLiouvilleFunctionAndItsSummatoryFunction
2008-06-04 18:55:38
2008-06-04 18:55:38
Data Structure
Liouville function
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The following table lists the values of the Liouville function $\lambda(n)$ and the summatory Liouville function $L(n)$ for $0 < n < 101$. The Liouville function is defined as $\lambda(n) = (-1)^{\Omega(n)}$ (where $\Omega(n)$ is the number of nondistinct prime factors function). The matching summatory function for the Liouville function is $$L(n) = \sum_{i = 1}^n \lambda(i).$$
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|r|}
$n$ & $\lambda(n)$ & $L(n)$ & $n$ & $\lambda(n)$ & $L(n)$ & $n$ & $\lambda(n)$ & $L(n)$ & $n$ & $\lambda(n)$ & $L(n)$ \\
1 & 1 & 1 & 26 & 1 & 0 & 51 & 1 & $-5$ & 76 & $-1$ & $-8$ \\
2 & $-1$ & 0 & 27 & $-1$ & $-1$ & 52 & $-1$ & $-6$ & 77 & 1 & $-7$ \\
3 & $-1$ & $-1$ & 28 & $-1$ & $-2$ & 53 & $-1$ & $-7$ & 78 & $-1$ & $-8$ \\
4 & 1 & 0 & 29 & $-1$ & $-3$ & 54 & 1 & $-6$ & 79 & $-1$ & $-9$ \\
5 & $-1$ & $-1$ & 30 & $-1$ & $-4$ & 55 & 1 & $-5$ & 80 & $-1$ & $$-1$0$ \\
6 & 1 & 0 & 31 & $-1$ & $-5$ & 56 & 1 & $-4$ & 81 & 1 & $-9$ \\
7 & $-1$ & $-1$ & 32 & $-1$ & $-6$ & 57 & 1 & $-3$ & 82 & 1 & $-8$ \\
8 & $-1$ & $-2$ & 33 & 1 & $-5$ & 58 & 1 & $-2$ & 83 & $-1$ & $-9$ \\
9 & 1 & $-1$ & 34 & 1 & $-4$ & 59 & $-1$ & $-3$ & 84 & 1 & $-8$ \\
10 & 1 & 0 & 35 & 1 & $-3$ & 60 & 1 & $-2$ & 85 & 1 & $-7$ \\
11 & $-1$ & $-1$ & 36 & 1 & $-2$ & 61 & $-1$ & $-3$ & 86 & 1 & $-6$ \\
12 & $-1$ & $-2$ & 37 & $-1$ & $-3$ & 62 & 1 & $-2$ & 87 & 1 & $-5$ \\
13 & $-1$ & $-3$ & 38 & 1 & $-2$ & 63 & $-1$ & $-3$ & 88 & 1 & $-4$ \\
14 & 1 & $-2$ & 39 & 1 & $-1$ & 64 & 1 & $-2$ & 89 & $-1$ & $-5$ \\
15 & 1 & $-1$ & 40 & 1 & 0 & 65 & 1 & $-1$ & 90 & 1 & $-4$ \\
16 & 1 & 0 & 41 & $-1$ & $-1$ & 66 & $-1$ & $-2$ & 91 & 1 & $-3$ \\
17 & $-1$ & $-1$ & 42 & $-1$ & $-2$ & 67 & $-1$ & $-3$ & 92 & $-1$ & $-4$ \\
18 & $-1$ & $-2$ & 43 & $-1$ & $-3$ & 68 & $-1$ & $-4$ & 93 & 1 & $-3$ \\
19 & $-1$ & $-3$ & 44 & $-1$ & $-4$ & 69 & 1 & $-3$ & 94 & 1 & $-2$ \\
20 & $-1$ & $-4$ & 45 & $-1$ & $-5$ & 70 & $-1$ & $-4$ & 95 & 1 & $-1$ \\
21 & 1 & $-3$ & 46 & 1 & $-4$ & 71 & $-1$ & $-5$ & 96 & 1 & 0 \\
22 & 1 & $-2$ & 47 & $-1$ & $-5$ & 72 & $-1$ & $-6$ & 97 & $-1$ & $-1$ \\
23 & $-1$ & $-3$ & 48 & $-1$ & $-6$ & 73 & $-1$ & $-7$ & 98 & $-1$ & $-2$ \\
24 & 1 & $-2$ & 49 & 1 & $-5$ & 74 & 1 & $-6$ & 99 & $-1$ & $-3$ \\
25 & 1 & $-1$ & 50 & $-1$ & $-6$ & 75 & $-1$ & $-7$ & 100 & 1 & $-2$ \\
\end{tabular}