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A303745 Totients t where gcd({x: phi(x)=t}) > 1.

%I A303745 #54 Nov 24 2024 11:28:40
%S A303745 10,22,28,30,44,46,52,54,56,58,66,70,78,82,92,102,104,106,110,116,126,
%T A303745 130,136,138,140,148,150,164,166,172,178,184,190,196,198,204,208,210,
%U A303745 212,220,222,226,228,238,250,260,262,268,270,282,292,294,296,306
%N A303745 Totients t where gcd({x: phi(x)=t}) > 1.
%C A303745 If the least solution of phi(x)=t is prime then gcd({x: phi(x)=t}) is prime.
%C A303745 If gcd({x: phi(x)=t}) > 1 is not prime then the least solution of phi(x)=t is not prime.
%C A303745 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
%H A303745 Robert Israel, <a href="/A303745/b303745.txt">Table of n, a(n) for n = 1..10000</a>
%H A303745 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%H A303745 Maxim Rytin, <a href="http://library.wolfram.com/infocenter/MathSource/696/">Finding the Inverse of Euler Totient Function</a>, Wolfram Library Archive, 1999.
%F A303745 gcd({x: phi(x)=t}) > 1.
%e A303745 10 is a term because the greatest common divisor of 11 and 22, the solutions of phi(10) is 11.
%e A303745 2 is not a term because the greatest common divisor of 3, 4 and 6, the solutions of phi(2) is 1.
%p A303745 filter:= proc(n) local L;
%p A303745 L:= numtheory:-invphi(n);
%p A303745 L <> [] and igcd(op(L)) > 1
%p A303745 end proc:
%p A303745 select(filter, [seq(i,i=2..1000, 2)]); # _Robert Israel_, Jun 26 2018
%t A303745 Select[Range[2, 1000, 2], GCD@@invphi[#] > 1&] (* _Jean-François Alcover_, Jan 31 2023, using Maxim Rytin's invphi program *)
%o A303745 (PARI) isok(n) = gcd(invphi(n)) > 1; \\ _Michel Marcus_, May 13 2018
%Y A303745 Cf. A000010, A002202, A032447, A297475, A007367.
%K A303745 nonn
%O A303745 1,1
%A A303745 _Torlach Rush_, Apr 29 2018