proposed
approved
editing
Cf. A087808 (a left inverse), A156552, A260443, A277189 (odd bisection).
a(2n) = 2*a(n).
A000120(a(n)) = A002487(n).
Cf. also A000079, A000120, A000225, A002450, A002487, A003754, A073491, A247648, A260442, A277010, A277012, A276081.
Antti Karttunen: Of course, forgot this, almost by definition:
For all n >= 1, a(A000225(n)) = A002450(n).
Antti Karttunen: Surely has still many other interesting or semi-interesting connections...
Cf. also A000079, A000225, A002450, A003754, A073491, A247648, A260442, A277010, A277012, A276081.