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Search: id:A113766
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| A113766 |
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a(n) is the product of those primes which divide some iterate of the Euler totient function but do not divide n itself. |
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1
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| 1, 1, 2, 1, 2, 1, 6, 1, 2, 1, 10, 1, 6, 3, 2, 1, 2, 1, 6, 1, 2, 5, 110, 1, 2, 3, 2, 3, 42, 1, 30, 1, 10, 1, 6, 1, 6, 3, 2, 1, 10, 1, 42, 5, 2, 55, 2530, 1, 6, 1, 2, 3, 78, 1, 2, 3, 2, 21, 1218, 1, 30, 15, 2, 1, 6, 5, 330, 1, 110, 3, 210, 1, 6, 3, 2, 3, 30, 1, 78, 1, 2, 5, 410, 1, 2, 21, 14, 5, 110
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) = product of primes p such that p does not divide n but p divides phi(n)*phi(phi(n))*phi(phi(phi(n)))...
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REFERENCES
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Florian Luca and Carl Pomerance, Irreducible radical extensions and Euler-function chains, pp. 351-362 in Combinatorial Number Theory, Landman et al., eds., de Gruyter, 2007 and in Integers, 7(2) (2007), paper A25.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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EXAMPLE
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E.g. phi(21)=12, phi(12)=4, phi(4)=2, phi(2)=1, so the only candidates are 2 and 3. But 3|21, so a(21)=2.
phi(43)=42, phi(42)=12, etc., so the candidates are 2, 3, 7, none of which divide 43, so a(43)=42.
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MATHEMATICA
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f[n_] := Times @@ Select[First /@ FactorInteger[Times @@ FixedPointList[ EulerPhi@# &, n]], Mod[n, # ] != 0 &]; Array[f, 90] - Robert G. Wilson v (rgwv(at)rgwv.com), Jul 08 2006
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CROSSREFS
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Sequence in context: A071416 A053589 A055770 this_sequence A112623 A130675 A163820
Adjacent sequences: A113763 A113764 A113765 this_sequence A113767 A113768 A113769
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), based on an email message from R. K. Guy, Jan 19 2006
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EXTENSIONS
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Corrected and extended by Robert G. Wilson v (rgwv(at)rgwv.com), Jul 08 2006
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