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

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

Offset

1,3

Comments

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)))...

Links

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

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.

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, Jul 08 2006 *)

Prog

(PARI) a(n)=my(s=n, v=[]~); while(s>1, v=concat(v, factor(s=eulerphi(s))[, 1])); v=setminus(vecsort(v~, , 8), factor(n)[, 1]~); prod(i=1, #v, v[i]) \\ Charles R Greathouse IV, Feb 04 2013

Crossrefs

Sequence in context: A055770 A225821 A368777 * A204992 A186726 A205405

Adjacent sequences: A113763 A113764 A113765 * A113767 A113768 A113769

Keyword

nonn,easy

Author

N. J. A. Sloane, based on an email message from R. K. Guy, Jan 19 2006

Extensions

Corrected and extended by Robert G. Wilson v, Jul 08 2006

Status

approved