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A326113
Numbers requiring 4 central factorizations to reach prime factorization.
3
512, 544, 608, 640, 704, 736, 768, 800, 832, 864, 880, 896, 920, 928, 960, 992, 1000, 1024, 1040, 1056, 1088, 1120, 1152, 1160, 1184, 1200, 1216, 1240, 1248, 1280, 1312, 1320, 1344, 1360, 1376, 1392, 1400, 1408, 1440, 1472, 1480, 1488, 1504, 1520, 1536, 1560
OFFSET
1,1
COMMENTS
Central factorization is defined at A308427. This sequence is row 5 of the array at A308427.
LINKS
EXAMPLE
The 1st central factorization of 544 is 17*32; the 2nd is 17*(4*8); the 3rd is 17*(4*(2*4)); the 4th is 17*(4*(2*(2*2))), is the prime factorization of 544.
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