OFFSET
1,2
COMMENTS
n such that the congruence x^3 == 1 mod(n) has only the trivial solution x=1 i.e. A060839(n) = 1 . Complement of sequence A066498.
Let U(n) be the group of positive integers coprime to n under mod n multiplication. Let U(n)^3 = {x^3: x is an element of U(n)}. These are the n such that U(n) = U(n)^3. - Geoffrey Critzer, Jun 07 2015
In other words, numbers divisible neither by 9 nor by any primes of the form 6k+1. - Ivan Neretin, Sep 03 2015
The asymptotic density of this sequence is 0 (Dressler, 1975). - Amiram Eldar, Jul 23 2020
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Robert E. Dressler, A property of the phi and sigma_j functions, Compositio Mathematica, Vol. 31, No. 2 (1975), pp. 115-118.
Kevin Ford, Florian Luca, and Pieter Moree, Values of the Euler phi-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields, arXiv:1108.3805 [math.NT], 2011-2012.
FORMULA
a(n) ~ k n sqrt(log(n)) for some constant k. k appears to be around 1.08. [Charles R Greathouse IV, Feb 14 2012]
MAPLE
select(t -> numtheory:-phi(t) mod 3 <> 0, [$1..1000]); # Robert Israel, Sep 04 2015
MATHEMATICA
Prepend[Position[Table[Union[Select[Range[n], CoprimeQ[#, n] &]] ==
Union[Mod[Select[Range[n], CoprimeQ[#, n] &]^3, n]], {n, 1, 155}], True], 1] // Flatten (* Geoffrey Critzer, Jun 07 2015 *)
Select[Range[140], !Divisible[EulerPhi[#], 3]&] (* Harvey P. Dale, Sep 23 2017 *)
PROG
(PARI) is(n)=eulerphi(n)%3 \\ Charles R Greathouse IV, Feb 04 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 03 2003
EXTENSIONS
More terms from Ray Chandler, Nov 05 2003
STATUS
approved