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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 (list; graph; refs; listen; history; text; internal format)
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

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

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 A253559 A136167

Adjacent sequences:  A308424 A308425 A308426 * A308428 A308429 A308430

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 03 2019

STATUS

approved

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Last modified June 23 12:05 EDT 2021. Contains 345401 sequences. (Running on oeis4.)