ThomaeFunction

\documentclass{article}
\usepackage{tikz}

\makeatletter
\pgfmathdeclarefunction*{gcd}{2}{%
  \begingroup
    \pgfmathcontinuelooptrue
    \pgfmath@xa=#1pt\relax % <-
    \pgfmath@xb=#2pt\relax % <-
    \ifdim\pgfmath@xa=0pt\relax
      \pgfmathcontinueloopfalse
      \pgfmath@xa=\pgfmath@xb
    \fi
    \ifdim\pgfmath@xb=0pt\relax
      \pgfmathcontinueloopfalse
      \pgfmath@xb=\pgfmath@xa
    \fi
    \ifdim\pgfmath@xa<0pt\relax
      \pgfmath@xa=-\pgfmath@xa
    \fi
    \ifdim\pgfmath@xb<0pt\relax
      \pgfmath@xb=-\pgfmath@xb
    \fi
    \loop
      \ifpgfmathcontinueloop
      \ifdim\pgfmath@xa=\pgfmath@xb
        \pgfmathcontinueloopfalse
      \else
        \ifdim\pgfmath@xa>\pgfmath@xb
          \advance\pgfmath@xa by-\pgfmath@xb\relax
        \else
          \advance\pgfmath@xb by-\pgfmath@xa\relax
        \fi
      \fi
    \repeat
    \pgfmathparse{int(\pgfmath@xa)}%
    \pgfmath@smuggleone\pgfmathresult
  \endgroup}
\makeatother

\begin{document}
\begin{center}
	\begin{tikzpicture}[scale=8]
	\draw [-stealth] (-0.1,0) -- (1.1,0);
	\draw [-stealth] (0,-0.1) -- (0,0.6);
	\foreach \X in {1,...,7}
	{\ifnum\X=1
		\else
		\draw (0.02,1/\X) -- (-0.02,1/\X) node[left,xshift={(-(1+pow(-1,\X)))*3pt}]{$\frac{1}{\X}$};
		\fi
	}
	\foreach \X [evaluate=\X as \Ymax using {int(\X-1)}]in {95,94,...,2}%Το μέγεθος του πρώτου όρου καθορίζει το πλήθος των κουκκίδων, άρα και την απόσταση του «τριγώνου» από τον χ'χ.
	{\foreach \Y in {1,...,\Ymax}
		{\ifnum\X<6
			\draw (\Y/\X,0.02) -- (\Y/\X,-0.02) node[below,fill=white]{$\frac{\Y}{\X}$};
			\else
			\draw[ultra thin] (\Y/\X,0.01) -- (\Y/\X,-0.01);
			\fi
			\pgfmathtruncatemacro{\TST}{gcd(\X,\Y)}
			\ifnum\TST=1
			\fill ({\Y/\X},1/\X) circle(0.05pt); %μέγεθος κουκκίδων
			\fi
		}
	}
	\foreach \X in {0,1,...,80}
	{\fill (\X/80,0) circle(0.05pt); } %μέγεθος κουκκίδων
	\end{tikzpicture}
\end{center}
\end{document}