OFFSET
1,8
COMMENTS
Consider the binary tree illustrated in A005940: If we start from any n, computing successive iterations of A252463 until 1 is reached (i.e., we are traversing level by level towards the root of the tree, starting from that vertex of the tree where n is located), a(n) gives the number of even numbers > 2 encountered on the path (i.e., excluding the 2 from the count but including the starting n if it was even).
The number of pairs in any factorization tree of n. For example, a possible factorization tree of 12 is 12 -> (4*3) -> (2*2)*3. There are 2 pairs in this factor tree: (4*3) and (2*2). Thus, a(12) - 1 = 3 - 1 = 2. - Melvin Peralta, Aug 29 2016
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..8192
FORMULA
MATHEMATICA
a[1] = a[2] = 0; a[n_] := a[n] = If[EvenQ@ n, 1 + a[n/2], a[Times @@ Power[Which[# == 1, 1, # == 2, 1, True, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger@ n]]; Array[a, 120] (* Michael De Vlieger, Aug 30 2016 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 21 2014
STATUS
approved