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A326112
Numbers requiring 3 central factorizations to reach prime factorization.
3
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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 09 2019
STATUS
approved