From: Allan Wechsler <acwacw@gmail.com> Date: 7/4/20, 4:35 PM

If it is easy for you to do, I would like to see a linear/linear version.

Belatedly, I've added the following bits at http://www.mac-guyver.com/switham/2020/07/OEIS_A001414/ o some linear/linear plots, o cut-off histograms of the a() values, o the (short) Python code (but also the necessary factoring code), o well it's a primitive web page now. Stopping n in the histogram is traumatic-- at a given N cutoff, early values of a(n < N) have appeared as many times as they ever will, and that section of the plot is very smooth, but beyond that it's like the trail of a rocket that exploded during ascent... oh yeah use OEIS... The full histogram is http://oeis.org/A000607 That math looks interesting in itself.

My theory has to do with A056239; this is very similar in concept to A001414, but instead of summing the primes themselves, you sum the *indices* of the primes, so for 84 = 2 * 2 * 3 * 7, the value is 1 + 1 + 2 + 4 = 8. It's possible that the "feathers" are formed by classes of integers which share the same A056239 value, so you might try doing a plot where points are assigned colors based on A056239.

I have not done this. I imagine one can just keep rotating the hue by 137.508 degrees... --Steve