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A287841
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Number of iterations of number of distinct prime factors (A001221) needed to reach 1 starting at n (n is counted).
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1
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1, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 3, 2, 2, 3, 2, 3, 3, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = a(omega(n)) + 1 for n > 1, where omega() is the number of distinct prime factors.
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EXAMPLE
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If n = 6 the trajectory is {6, 2, 1}. Its length is 3, thus a(6) = 3.
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MATHEMATICA
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f[n_] := Length[NestWhileList[ PrimeNu, n, # != 1 &]]; Array[f, 105]
a[1] = 1; a[n_] := a[n] = a[PrimeNu[n]] + 1; Table[a[n], {n, 105}]
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PROG
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(Python)
from sympy import primefactors
def a(n): return 1 if n==1 else a(len(primefactors(n))) + 1 # Indranil Ghosh, Jun 03 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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