A071388 Numbers k such that the cardinality of the set of solutions to phi(x) = k is a prime.

1, 2, 8, 10, 20, 22, 28, 30, 32, 44, 46, 48, 52, 54, 56, 58, 66, 70, 72, 78, 82, 92, 96, 102, 104, 106, 110, 116, 120, 126, 130, 132, 136, 138, 140, 148, 150, 156, 164, 166, 172, 178, 190, 196, 198, 204, 210, 212, 216, 220, 222, 226, 228, 238, 240, 250, 260, 262

Offset: 1

Author

Labos Elemer, May 23 2002

Keywords

• nonn

Comments

All terms except 1 are even. - Robert Israel, Mar 29 2020

Examples

			InvPhi(48) = {65,104,105,112,130,140,144,156,168,180,210} has 11 terms, so 48 is a term.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A000010, A007366, A007367, A014197, A058277, A060668, A060670, A060674, A063512, A071386-A071389.

Programs

Maple

filter:= n -> isprime(nops(numtheory:-invphi(n))):
select(filter, [$1..400]); # Robert Israel, Mar 29 2020

PARI

is(k) = isprime(invphiNum(k)); \\ Amiram Eldar, Nov 15 2024, using Max Alekseyev's invphi.gp