|
Search: id:A113766
|
|
|
| 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 A057568
Adjacent sequences: A113763 A113764 A113765 this_sequence A113767 A113768 A113769
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
njas, 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
|
|
|
Search completed in 0.002 seconds
|
