A326112 - OEIS

%I #4 Jun 09 2019 13:10:22

%S 32,40,48,56,64,72,80,84,88,96,104,108,112,120,128,132,136,144,152,

%T 156,160,162,168,176,180,184,192,198,200,204,208,216,220,224,228,232,

%U 234,240,243,248,252,256,260,264,270,272,276,280,288,296,297,300,304,306

%N Numbers requiring 3 central factorizations to reach prime factorization.

%C Central factorization is defined at A308427.  This sequence is row 4 of the array at A308427.

%H Clark Kimberling, <a href="/A326112/b326112.txt">Table of n, a(n) for n = 1..10000</a>

%e The 1st central factorization of 32 is 4*8; the 2nd is (2*2)*(2*4); the 3rd is (2*2)*(2*(2*2)), which is the prime factorization of 32.

%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, A326113.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jun 09 2019