%I #4 Jun 09 2019 13:10:28
%S 512,544,608,640,704,736,768,800,832,864,880,896,920,928,960,992,1000,
%T 1024,1040,1056,1088,1120,1152,1160,1184,1200,1216,1240,1248,1280,
%U 1312,1320,1344,1360,1376,1392,1400,1408,1440,1472,1480,1488,1504,1520,1536,1560
%N Numbers requiring 4 central factorizations to reach prime factorization.
%C Central factorization is defined at A308427. This sequence is row 5 of the array at A308427.
%H Clark Kimberling, <a href="/A326113/b326113.txt">Table of n, a(n) for n = 1..4000</a>
%e The 1st central factorization of 544 is 17*32; the 2nd is 17*(4*8); the 3rd is 17*(4*(2*4)); the 4th is 17*(4*(2*(2*2))), is the prime factorization of 544.
%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, A326111, A326112.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jun 09 2019