%I #24 Mar 27 2020 15:51:53
%S 0,1,2,1,3,2,4,1,2,3,6,2,5,4,3,1,7,2,8,3,4,6,10,2,3,5,2,4,9,3,12,1,6,
%T 7,4,2,11,8,5,3,13,4,14,6,3,10,16,2,4,3,7,5,15,2,6,4,8,9,18,3,17,12,4,
%U 1,5,6,20,7,10,4,22,2,19,11,3,8,6,5,24,3,2,13,26,4,7,14,9,6,21,3,5,10,12,16,8,2,23,4,6,3,25,7,28,5,4
%N a(1) = 0, and for n > 2, a(n) = a(A332893(n)) + A000035(n).
%C a(n) tells how many odd numbers are encountered when map x -> A332893(x) is used to traverse from n to 1, the root of the binary tree A332815. This count includes both the starting n itself if it is odd, but excludes 1 where the iteration ends.
%C a(n) also gives the index of the largest prime factor (A061395) in A332808(n), which is the inverse permutation of A108548 (see also A108546).
%H Antti Karttunen, <a href="/A332899/b332899.txt">Table of n, a(n) for n = 1..16384</a>
%H Antti Karttunen, <a href="/A332899/a332899.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F a(1) = 0, and for n > 1, a(n) = a(A332893(n)) + A000035(n).
%F a(n) = A000120(A332811(n)).
%F a(n) = A061395(A332808(n)).
%F a(n) = A332897(n) + A332898(n).
%F a(n) <= A332894(n).
%F For all n > 1, a(n) = 1 + A080791(A332816(n)).
%o (PARI) A332899(n) = if(1==n,0,A332899(A332893(n)) + (n%2));
%Y Cf. A000035, A061395, A080791, A332808, A332811, A332815, A332816, A332893, A332894, A332897, A332898.
%Y Cf. A000079 (after its initial term, gives the positions of 1's).
%K nonn
%O 1,3
%A _Antti Karttunen_, Mar 04 2020