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A019269
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Let Dedekind's psi(m) = product of (p+1)p^(e-1) for primes p, where p^e is a factor of m. Iterating psi(m) eventually results in a number of form 2^a*3^b. a(n) is the number of steps to reach such a number.
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5
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0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 2, 1, 1, 0, 1, 0, 2, 1, 1, 1, 1, 0, 2, 2, 0, 1, 2, 1, 1, 0, 1, 1, 1, 0, 3, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 0, 2, 2, 1, 2, 1, 0, 1, 1, 2, 2, 2, 1, 2, 1, 1, 0, 2, 1, 2, 1, 1, 1, 1, 0, 4, 3, 2, 2, 1, 2, 2, 1, 0, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 0, 3, 2, 1
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OFFSET
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1,13
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COMMENTS
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REFERENCES
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Peter Giblin, "Primes and Programming - an Introduction to Number Theory with Computation", page 118.
R. K. Guy, "Unsolved Problems in Number Theory", section B41.
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LINKS
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MATHEMATICA
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psi[n_] := Module[{pp, ee}, {pp, ee} = Transpose[FactorInteger[n]]; If[Max[pp] == 3, n, Times @@ (pp+1)*Times @@ (pp^(ee-1))]];
a[n_] := Length[NestWhileList[psi, n, FactorInteger[#][[-1, 1]] > 3&]] - 1;
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PROG
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(Haskell)
a019269 n = snd $ until ((== 1) . a065333 . fst)
(\(x, i) -> (a001615 x, i+1)) (n, 0)
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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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