OFFSET
1,1
COMMENTS
If the least solution of phi(x)=t is prime then gcd({x: phi(x)=t}) is prime.
If gcd({x: phi(x)=t}) > 1 is not prime then the least solution of phi(x)=t is not prime.
For known terms if the number of solutions of x: phi(x)=t is 2 or 3 then the least solution divides the greatest solution (see A297475). - Torlach Rush, Jul 03 2018
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Max Alekseyev, PARI scripts for various problems
Maxim Rytin, Finding the Inverse of Euler Totient Function, Wolfram Library Archive, 1999.
FORMULA
gcd({x: phi(x)=t}) > 1.
EXAMPLE
10 is a term because the greatest common divisor of 11 and 22, the solutions of phi(10) is 11.
2 is not a term because the greatest common divisor of 3, 4 and 6, the solutions of phi(2) is 1.
MAPLE
filter:= proc(n) local L;
L:= numtheory:-invphi(n);
L <> [] and igcd(op(L)) > 1
end proc:
select(filter, [seq(i, i=2..1000, 2)]); # Robert Israel, Jun 26 2018
MATHEMATICA
Select[Range[2, 1000, 2], GCD@@invphi[#] > 1&] (* Jean-François Alcover, Jan 31 2023, using Maxim Rytin's invphi program *)
PROG
(PARI) isok(n) = gcd(invphi(n)) > 1; \\ Michel Marcus, May 13 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Torlach Rush, Apr 29 2018
STATUS
approved