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A303745 Totients t where gcd({x: phi(x)=t}) > 1. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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

PROG

(PARI) isok(n) = gcd(invphi(n)) > 1; \\ Michel Marcus, May 13 2018

CROSSREFS

Cf. A000010, A002202, A032447, A297475, A007367.

Sequence in context: A104865 A063555 A228010 * A303746 A303747 A007366

Adjacent sequences:  A303742 A303743 A303744 * A303746 A303747 A303748

KEYWORD

nonn

AUTHOR

Torlach Rush, Apr 29 2018

STATUS

approved

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Last modified November 19 22:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)