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A326111 Numbers requiring 2 central factorizations to reach prime factorization. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 15 17:45 EDT 2021. Contains 348033 sequences. (Running on oeis4.)