Problems
GCD Extreme
GCD Extreme
Given the value of \textbf{n}, you have to find the value of \textbf{G}, where
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Here \textbf{GCD}(\textbf{i, j}) means the greatest common divisor of integer \textbf{i} and integer \textbf{j}.
For those who have trouble understanding summation notation, the meaning of \textbf{G} is given in the following code:
G=0;for(i=1; i < n;i++)for(j=i+1;j<=n;j++)\{ G+=GCD(i,j);\}/*Here GCD() is a function that finds the greatest common divisor of the two input numbers*/
\InputFile
The input file contains at most \textbf{20000} lines of inputs. Each line contains an integer \textbf{n} (\textbf{1} < \textbf{n} < \textbf{200001}). The last line contains \textbf{n} = \textbf{0} and is not processed.
\OutputFile
For each line of input produce one line of output. This line contains the value of \textbf{G} for the corresponding \textbf{n}. The value of \textbf{G} will fit in a \textbf{64}-bit signed integer.
Input example #1
10 100 20000 0
Output example #1
67 13015 1153104356