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A113766 a(n) is the product of those primes which divide some iterate of the Euler totient function but do not divide n itself. +0
1
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)
OFFSET

1,3

COMMENT

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)))...

REFERENCES

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.

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS

Sequence in context: A071416 A053589 A055770 this_sequence A112623 A130675 A163820

Adjacent sequences: A113763 A113764 A113765 this_sequence A113767 A113768 A113769

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com), based on an email message from R. K. Guy, Jan 19 2006

EXTENSIONS

Corrected and extended by Robert G. Wilson v (rgwv(at)rgwv.com), Jul 08 2006

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Last modified December 16 13:01 EST 2009. Contains 170825 sequences.


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