A326112 Numbers requiring 3 central factorizations to reach prime factorization.

32, 40, 48, 56, 64, 72, 80, 84, 88, 96, 104, 108, 112, 120, 128, 132, 136, 144, 152, 156, 160, 162, 168, 176, 180, 184, 192, 198, 200, 204, 208, 216, 220, 224, 228, 232, 234, 240, 243, 248, 252, 256, 260, 264, 270, 272, 276, 280, 288, 296, 297, 300, 304, 306

Offset

1,1

Comments

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

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Example

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.

Mathematica

f[n_] := Last[Select[Divisors[n], # <= Sqrt[n] &]];
a[1] = 0; a[2] = 0; a[n_] := If[f[n] == 1, 0, 1 + Max[a[f[n]], a[n/f[n]]]];
u = Table[a[n], {n, 1, 1000}];
Flatten[Position[u, 2]] (* A326111 *)
Flatten[Position[u, 3]] (* A326112 *)
Flatten[Position[u, 4]] (* A326113 *)

Crossrefs

Cf. A000040, A308427, A326111, A326113.

Sequence in context: A039778 A354422 A217060 * A363530 A240246 A167309

Adjacent sequences: A326109 A326110 A326111 * A326113 A326114 A326115

Keyword

nonn,easy

Author

Clark Kimberling, Jun 09 2019

Status

approved