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A075167
Number of edges in each rooted plane tree produced with the unranking algorithm presented in A075166, which is based on prime factorization.
11
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
1,3
COMMENTS
Each n occurs A000108(n) times in total.
LINKS
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. also A106490.
Sequence in context: A384384 A230697 A322163 * A253555 A252464 A324861
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 13 2002
EXTENSIONS
More terms from Antti Karttunen, May 09 2005
STATUS
approved