A253889 a(n) = A048673(floor(A064216(n)/2)).

1, 1, 1, 2, 2, 3, 4, 3, 8, 14, 4, 13, 5, 5, 7, 17, 6, 6, 18, 7, 38, 32, 8, 28, 23, 9, 15, 11, 10, 26, 16, 11, 41, 53, 12, 33, 39, 13, 10, 113, 14, 43, 12, 15, 22, 63, 16, 25, 59, 17, 203, 74, 18, 48, 30, 19, 188, 50, 20, 122, 68, 21, 9, 149, 22, 138, 83, 23, 60, 86, 24, 35, 29, 25, 73, 62, 26, 24, 123, 27, 27, 128, 28, 313

Offset

1,4

Comments

When A048673 is represented as a binary tree, then any non-root node k (>= 2) which contains value n = A048673(k) has as its parent a(n) = A048673(floor(k/2)).

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

Formula

a(n) = A048673(floor(A064216(n)/2)).

Other identities. For all n >= 0:

a(3n+2) = n+1.

Mathematica

f[n_] := Times @@ Power[If[# == 1, 1, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger[2 n - 1]; g[n_] := (Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] + 1)/2 &@ Transpose@ FactorInteger@ n; Array[Floor@ g[Floor[f[#]/2]] &, 84] (* Michael De Vlieger, Sep 16 2017 *)

Prog

(Scheme) (define (A253889 n) (A048673 (floor->exact (/ (A064216 n) 2))))

Crossrefs

Cf. A048673, A064216, A253888, A253893.

Sequence in context: A284113 A324480 A164975 * A228754 A171830 A071506

Adjacent sequences: A253886 A253887 A253888 * A253890 A253891 A253892

Keyword

nonn

Author

Antti Karttunen, Jan 22 2015

Status

approved