Problem
2020 AMC 8 Problem 22
When a positive integer N is fed into a machine, the output is a number calculated according to the rule shown below.
![[asy] size(300); defaultpen(linewidth(0.8)+fontsize(13)); real r = 0.05; draw((0.9,0)--(3.5,0),EndArrow(size=7)); filldraw((4,2.5)--(7,2.5)--(7,-2.5)--(4,-2.5)--cycle,gray(0.65)); fill(circle((5.5,1.25),0.8),white); fill(circle((5.5,1.25),0.5),gray(0.65)); fill((4.3,-r)--(6.7,-r)--(6.7,-1-r)--(4.3,-1-r)--cycle,white); fill((4.3,-1.25+r)--(6.7,-1.25+r)--(6.7,-2.25+r)--(4.3,-2.25+r)--cycle,white); fill((4.6,-0.25-r)--(6.4,-0.25-r)--(6.4,-0.75-r)--(4.6,-0.75-r)--cycle,gray(0.65)); fill((4.6,-1.5+r)--(6.4,-1.5+r)--(6.4,-2+r)--(4.6,-2+r)--cycle,gray(0.65)); label("$N$",(0.45,0)); draw((7.5,1.25)--(11.25,1.25),EndArrow(size=7)); draw((7.5,-1.25)--(11.25,-1.25),EndArrow(size=7)); label("if $N$ is even",(9.25,1.25),N); label("if $N$ is odd",(9.25,-1.25),N); label("$\frac N2$",(12,1.25)); label("$3N+1$",(12.6,-1.25)); [/asy]](/static/aops/640f84b97add51c20f2c5af092b282884530e77b.png)
For example, starting with an input of N=7, the machine will output 3 \cdot 7 +1 = 22. Then if the output is repeatedly inserted into the machine five more times, the final output is 26. 7 \to 22 \to 11 \to 34 \to 17 \to 52 \to 26When the same 6-step process is applied to a different starting value of N, the final output is 1. What is the sum of all such integers N? N \to \underline{\ \ \ } \to \underline{\ \ \ } \to \underline{\ \ \ } \to \underline{\ \ \ } \to \underline{\ \ \ } \to 1
\textbf{(A) }73 \qquad \textbf{(B) }74 \qquad \textbf{(C) }75 \qquad \textbf{(D) }82 \qquad \textbf{(E) }83
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