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%I #12 Jun 06 2019 15:29:15
%S 0,0,0,1,0,1,0,2,1,1,0,2,0,1,1,2,0,2,0,2,1,1,0,2,1,1,2,2,0,2,0,3,1,1,
%T 1,2,0,1,1,3,0,2,0,2,2,1,0,3,1,2,1,2,0,2,1,3,1,1,0,2,0,1,2,3,1,2,0,2,
%U 1,2,0,3,0,1,2,2,1,2,0,3,2,1,0,3,1,1
%N a(n) is the number of central factorizations needed to reach the prime factorization of n.
%C The central factorization of a positive integer m is m*(n/m), where m is the greatest divisor of n that is <= sqrt(n).
%H Clark Kimberling, <a href="/A308427/b308427.txt">Table of n, a(n) for n = 1..10000</a>
%e 32 = 4*8 = (2*2)*(2*4) = (2*2)*(2*(2*2)), so that a(32) = 3.
%t f[n_] := Last[Select[Divisors[n], # <= Sqrt[n] &]];
%t a[1] = 0; a[2] = 0; a[n_] := If[f[n] == 1, 0, 1 + Max[a[f[n]], a[n/f[n]]]];
%t Table[a[n], {n, 1, 60}]
%Y Cf. A000040.
%K nonn,easy
%O 1,8
%A _Clark Kimberling_, Jun 03 2019
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