A075167 - OEIS

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

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OFFSET

1,3

COMMENTS

Each n occurs A000108(n) times in total.

LINKS

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

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)

PROG

(Scheme, with memoization-macro definec)

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

;; Antti Karttunen, Jan 16 2015

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.

Sequence in context: A099053 A230697 A322163 * A253555 A252464 A324861

Adjacent sequences: A075164 A075165 A075166 * A075168 A075169 A075170

KEYWORD

nonn

AUTHOR

Antti Karttunen, Sep 13 2002

EXTENSIONS

More terms from Antti Karttunen, May 09 2005

STATUS

approved