Lars Blomberg has discovered that if we start with any positive integer and repeatedly apply the map m > A320486(m^2) then we will eventually either:
 reach 0,
 reach one of the four fixed points 1, 1465, 4376, 89476 (this sequence),
 reach the period10 cycle shown in A321011, or
 reach the period9 cycle shown in A321012.
From Lars Blomberg, Nov 17 2018: (Start)
Verified by testing all possible 8877690 start values that these are the only fixed points and cycles.
Detailed counts are:
 561354 reach 0,
 963738 reach one of the four fixed points 1, 1465, 4376, 89476 (counts 946109, 434, 17065, 130),
 7271337 reach the period10 cycle, and
 81261 reach the period9 cycle. (End)
