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Number of edges in each rooted plane tree produced with the unranking algorithm presented in A075166, which is based on prime factorization.
11

%I #16 Jan 16 2015 10:18:52

%S 0,1,2,2,3,3,4,3,3,4,5,4,6,5,4,3,7,4,8,5,5,6,9,4,4,7,4,6,10,5,11,4,6,

%T 8,5,5,12,9,7,5,13,6,14,7,5,10,15,5,5,5,8,8,16,5,6,6,9,11,17,6,18,12,

%U 6,4,7,7,19,9,10,6,20,5,21,13,5,10,6,8,22,6,4,14,23,7,8,15,11,7,24,6,7,11

%N Number of edges in each rooted plane tree produced with the unranking algorithm presented in A075166, which is based on prime factorization.

%C Each n occurs A000108(n) times in total.

%H Antti Karttunen, <a href="/A075167/b075167.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A106457(A106442(n)). - _Antti Karttunen_, May 09 2005

%F From _Antti Karttunen_, Jan 16 2015: (Start)

%F a(1) = 0; for n>1: a(n) = a(A071178(n)) + (A061395(n) - A061395(A051119(n))) + A253783(A051119(n)).

%F Other identities.

%F For all n >= 2, a(n) = A055642(A075166(n))/2. [Half of the number of decimal digits in A075166(n).]

%F For all n >= 2, a(n) = A029837(1+A075165(n))/2. [Half of the binary width of A075165(n).]

%F For all n >= 1, a(n) = A000120(A075165(n)). [Thus also the binary weight of A075165(n), because half of the bits are zeros.]

%F (End)

%o (Scheme, with memoization-macro definec)

%o (definec (A075167 n) (if (= 1 n) 0 (+ (A075167 (A071178 n)) (- (A061395 n) (A061395 (A051119 n))) (A253783 (A051119 n)))))

%o ;; _Antti Karttunen_, Jan 16 2015

%Y Permutation of A072643 and A106457.

%Y A253782 gives the positions where this sequence differs from A252464 (first time at n=16).

%Y Cf. A000108, A000120, A029837, A055642, A051119, A061395, A071178, A075165, A075166, A106442, A253783.

%Y Cf. also A106490.

%K nonn

%O 1,3

%A _Antti Karttunen_, Sep 13 2002

%E More terms from _Antti Karttunen_, May 09 2005