Draft of number-theory macro

\def\makeatletter{\catcode `\@11\relax}
\def\makeatother{\catcode `\@12\relax}

\makeatletter

\newif\ifdivisible
\newcount\testMod@n
\def\testMod#1#2{% sets divisible = [#1 mod #2 == 0]
	\testMod@n=#1%
	\divide\testMod@n by#2%
	\multiply\testMod@n by#2%
	\ifnum#1=\testMod@n%
		\divisibletrue%
	\else%
		\divisiblefalse%
	\fi%
}

\newcount\divisorpower
\newcount\getDivisorPower@n
\def\getDivisorPower#1#2{% sets divisorpower = {max a such that #2^a divides #1} and getDivisorPower@n = #1/#2^a
	\getDivisorPower@n=#1%
	\divisorpower=0%
	\testMod{\getDivisorPower@n}{#2}%
	\loop\ifdivisible%
		\advance\divisorpower by1%
		\divide\getDivisorPower@n by#2%
		\testMod{\getDivisorPower@n}{#2}%
	\repeat%
}

\newcount\numberpower
\newcount\getNumberPower@pow
\def\getNumberPower#1#2{% sets numberpower = #1^#2
	\numberpower=1
	\getNumberPower@pow=#2
	\loop\ifnum\getNumberPower@pow>0
		\multiply\numberpower by#1
		\advance\getNumberPower@pow by-1
	\repeat
	}

\newif\ifcanonical@more
\newcount\canonical@n
\newcount\canonical@i
\newcount\canonical@sqri

\def\canonical#1#2{% runs #2{p}{a} for each p^a such that divides #1 and p^{a+1} does not divide
	\canonical@n=#1%
	\canonical@i=2%
%
	\ifnum\canonical@n<4
		\canonical@morefalse%
	\else
		\canonical@moretrue%
	\fi%
%
	\loop\ifcanonical@more%
		{%
		\getDivisorPower{\canonical@n}{\canonical@i}%
		\ifnum\divisorpower>0%
			#2{\number\canonical@i}{\number\divisorpower}%
			\global\canonical@n=\getDivisorPower@n%
		\fi%
		}%
%
		\ifodd\canonical@i%
			\advance\canonical@i by2%
			\else%
			\advance\canonical@i by1%
		\fi%
		\canonical@sqri=\canonical@i%
		\multiply\canonical@sqri by\canonical@sqri%
%
		\ifnum\canonical@n<2
			\canonical@morefalse%
		\fi%
		\ifnum\canonical@n<\canonical@sqri%
			\canonical@morefalse%
		\fi%
	\repeat%
%
	\ifnum\canonical@n>1
		#2{\number\canonical@n}{1}%
	\fi
}

\def\printCanonHelper#1#2{\cdot#1^#2}
\def\printCanon#1{$$ #1 = 1\canonical{#1}{\printCanonHelper} $$}

\newcount\eulerPhi@v
\newcount\eulerPhi@p
\newcount\eulerPhi@a
\def\eulerPhiHelper#1#2{
	\eulerPhi@p=#1
	\eulerPhi@a=#2
	\advance\eulerPhi@a by-1
	\getNumberPower{\eulerPhi@p}{\eulerPhi@a}
	\advance\eulerPhi@p by-1
	\multiply\numberpower by\eulerPhi@p
	\global\multiply\eulerPhi@v by\numberpower
	}
\def\eulerPhi#1{
	\eulerPhi@v=1
	\canonical{#1}{\eulerPhiHelper}
	$$ \varphi(#1)= \number\eulerPhi@v $$
	}

\makeatother

\printCanon{1546275796}

\eulerPhi{1546275796}

\end