If you look the at the wikipedia page for the Euler totient function there is a graph of the Euler phi function up to 1000:
Out of the plot you can see various trend lines that appear to be linear.
Q1) Are these lines actually lines? (ie do all the points that appear to be on one line actually all solutions to some linear eqn?)
Q2) Given that they're lines and not just something that looks a bit like lines can they be described? and what points are on them?
Q3) Are the points that don't appear to be on lines actually just the first points on lines that would only be 'visible' if we zoomed out and evaluated the Euler phi up to (say) 10000 or whatever number is large enough.