A058341 Primes p such that phi(x) = p - 1 has more than 2 solutions.

3, 5, 7, 13, 17, 19, 37, 41, 43, 61, 73, 89, 97, 101, 109, 113, 157, 163, 181, 193, 233, 241, 257, 277, 281, 313, 337, 349, 353, 397, 401, 409, 421, 433, 449, 457, 461, 487, 521, 541, 577, 593, 601, 613, 617, 641, 661, 673, 701, 733, 757, 761, 769, 821, 829

Offset: 1

Author

Labos Elemer, Dec 14 2000

Keywords

• nonn

Comments

There are always at least 2 such values: p and 2p. - Franklin T. Adams-Watters, May 17 2010

Examples

			3 is a term since phi(x) = 3 - 1 = 2 has more than 2 solutions: 3, 4 and 6.
5 is a term since phi(x) = 5 - 1 = 4 has more than 2 solutions: 5, 8, 10 and 12.
		

Links

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

Crossrefs

Cf. A000010, A006093.

Cf. A014197, A058277, A005277. - Franklin T. Adams-Watters, May 17 2010

Programs

PARI

isok(p) = isprime(p) && #invphi(p-1) > 2; \\ Amiram Eldar, Mar 08 2025, using Max Alekseyev's invphi.gp (see links).