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A303745
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Totients t where gcd({x: phi(x)=t}) > 1.
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6
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10, 22, 28, 30, 44, 46, 52, 54, 56, 58, 66, 70, 78, 82, 92, 102, 104, 106, 110, 116, 126, 130, 136, 138, 140, 148, 150, 164, 166, 172, 178, 184, 190, 196, 198, 204, 208, 210, 212, 220, 222, 226, 228, 238, 250, 260, 262, 268, 270, 282, 292, 294, 296, 306
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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gcd({x: phi(x)=t}) > 1.
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EXAMPLE
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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.
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MAPLE
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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
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MATHEMATICA
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Select[Range[2, 1000, 2], GCD@@invphi[#] > 1&] (* Jean-François Alcover, Jan 31 2023, using Maxim Rytin's invphi program *)
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PROG
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(PARI) isok(n) = gcd(invphi(n)) > 1; \\ Michel Marcus, May 13 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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