A005361(A005361(n)) > 1

[Jonathan Post]

I don't see in OEIS:
n such that A005361(A005361(n))  > 1
16, 36, 48, 80, 81, 100, 112, 162, 176, 180, 196, 208, 216, 225, 240, ...
A005361(PRODUCT((p_i)^(e_i))) = PRODUCT(e^i).
A005361(PRODUCT((p_i)^(PRODUCT((p_j)^(e^j)))) = PRODUCT(e^j).
Depends only on prime signature of of n.
There should be an even more obvious characterization.