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A049108
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a(n) is the number of iterations of Euler phi function needed to reach 1 starting at n (n is counted).
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24
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1, 2, 3, 3, 4, 3, 4, 4, 4, 4, 5, 4, 5, 4, 5, 5, 6, 4, 5, 5, 5, 5, 6, 5, 6, 5, 5, 5, 6, 5, 6, 6, 6, 6, 6, 5, 6, 5, 6, 6, 7, 5, 6, 6, 6, 6, 7, 6, 6, 6, 7, 6, 7, 5, 7, 6, 6, 6, 7, 6, 7, 6, 6, 7, 7, 6, 7, 7, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 7, 6, 7, 8, 6, 8, 6, 7, 7, 8, 6, 7, 7, 7, 7, 7, 7, 8, 6, 7, 7, 8, 7, 8, 7, 7
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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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By the definition of a(n) we have for n >= 2 the recursion a(n) = a(Phi(n)) + 1. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 20 2001
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EXAMPLE
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If n=164 the trajectory is {164,80,32,16,8,4,2,1}. Its length is 8, thus a(164)=8.
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MAPLE
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local a, e;
e := n ;
a :=0 ;
while e > 1 do
a := a+1 ;
e := numtheory[phi](e) ;
end do:
1+a;
end proc:
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MATHEMATICA
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f[n_] := Length[NestWhileList[ EulerPhi, n, # != 1 &]]; Array[f, 105] (* Robert G. Wilson v, Feb 07 2012 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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STATUS
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approved
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