A075167 Number of edges in each rooted plane tree produced with the unranking algorithm presented in A075166, which is based on prime factorization.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Sep 13 2002

Keywords

• nonn

Comments

Each n occurs A000108(n) times in total.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Permutation of A072643 and A106457.

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

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

Cf. also A106490.

Formula

a(n) = A106457(A106442(n)). - Antti Karttunen, May 09 2005

From Antti Karttunen, Jan 16 2015: (Start)

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

Other identities.

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

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

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

(End)

Extensions

More terms from Antti Karttunen, May 09 2005