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%I #5 Jun 09 2019 13:10:16
%S 8,12,16,18,20,24,27,28,30,36,42,44,45,50,52,54,60,63,66,68,70,75,76,
%T 78,81,90,92,98,99,100,102,105,110,114,116,117,124,125,126,130,135,
%U 138,140,147,148,150,153,154,164,165,170,171,172,174,175,182,186,188
%N Numbers requiring 2 central factorizations to reach prime factorization.
%C Central factorization is defined at A308427. This sequence is row 3 of the array at A308427.
%H Clark Kimberling, <a href="/A326111/b326111.txt">Table of n, a(n) for n = 1..10000</a>
%e The 1st central factorization of 8 is 2*4; the 2nd is 2*(2*2), the prime factorization of 8.
%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 u = Table[a[n], {n, 1, 1000}];
%t Flatten[Position[u, 2]] (* A326111 *)
%t Flatten[Position[u, 3]] (* A326112 *)
%t Flatten[Position[u, 4]] (* A326113 *)
%Y Cf. A000040, A308427, A326112, A326113.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jun 09 2019
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