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A308427
a(n) is the number of central factorizations needed to reach the prime factorization of n.
4
0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 0, 2, 1, 1, 2, 2, 0, 2, 0, 3, 1, 1, 1, 2, 0, 1, 1, 3, 0, 2, 0, 2, 2, 1, 0, 3, 1, 2, 1, 2, 0, 2, 1, 3, 1, 1, 0, 2, 0, 1, 2, 3, 1, 2, 0, 2, 1, 2, 0, 3, 0, 1, 2, 2, 1, 2, 0, 3, 2, 1, 0, 3, 1, 1
OFFSET
1,8
COMMENTS
The central factorization of a positive integer m is m*(n/m), where m is the greatest divisor of n that is <= sqrt(n).
LINKS
EXAMPLE
32 = 4*8 = (2*2)*(2*4) = (2*2)*(2*(2*2)), so that a(32) = 3.
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]]]];
Table[a[n], {n, 1, 60}]
CROSSREFS
Cf. A000040.
Sequence in context: A257857 A339871 A276806 * A252736 A351416 A253559
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 03 2019
STATUS
approved