A326111 Numbers requiring 2 central factorizations to reach prime factorization.

8, 12, 16, 18, 20, 24, 27, 28, 30, 36, 42, 44, 45, 50, 52, 54, 60, 63, 66, 68, 70, 75, 76, 78, 81, 90, 92, 98, 99, 100, 102, 105, 110, 114, 116, 117, 124, 125, 126, 130, 135, 138, 140, 147, 148, 150, 153, 154, 164, 165, 170, 171, 172, 174, 175, 182, 186, 188

Offset

1,1

Comments

Central factorization is defined at A308427. This sequence is row 3 of the array at A308427.

Links

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

Example

The 1st central factorization of 8 is 2*4; the 2nd is 2*(2*2), the prime factorization of 8.

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, A326112, A326113.

Sequence in context: A341610 A337373 A166083 * A091375 A282671 A192991

Adjacent sequences: A326108 A326109 A326110 * A326112 A326113 A326114

Keyword

nonn,easy

Author

Clark Kimberling, Jun 09 2019

Status

approved