A253889 - OEIS

%I #14 Sep 17 2017 22:53:06

%S 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,

%T 26,16,11,41,53,12,33,39,13,10,113,14,43,12,15,22,63,16,25,59,17,203,

%U 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

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

%C 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)).

%H Antti Karttunen, <a href="/A253889/b253889.txt">Table of n, a(n) for n = 1..8192</a>

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

%F Other identities. For all n >= 0:

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

%t 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 *)

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

%Y Cf. A048673, A064216, A253888, A253893.

%K nonn

%O 1,4

%A _Antti Karttunen_, Jan 22 2015