A271983 The smaller of a pair n, m such that phi(n) = phi(m) and there is no other k such that phi(n) = phi(k).

1, 11, 23, 29, 31, 47, 53, 81, 59, 67, 71, 79, 83, 103, 107, 121, 127, 131, 137, 139, 149, 151, 167, 173, 179, 191, 197, 199, 211, 223, 227, 229, 239, 251, 263, 269, 271, 283, 293, 343, 307, 311, 317, 331, 361, 347, 359, 367, 373, 379, 383, 389, 419, 431, 439, 443, 463, 467, 479, 491, 499

Offset: 1

Author

Geoffrey Critzer, Apr 17 2016

Keywords

• nonn

Comments

If phi(x) = N has exactly two solutions, x = n and x = m, say (see A007366), it is conjectured that one of n and m is odd and the other even.

This sequence differs from A058340 in that it contains nonprime integers. The first few are 81, 121, 343, 361, 529, 649, 841, 961, 1219, 1331, 1537, 1633, ...

Examples

			81 is a term because phi(81) = phi(162) = 54 (= A007366(8)).
		

Crossrefs

Cf. A007366, A058340.

Programs

Mathematica

(* takes about 2 minutes, can return the sequence up to terms less than 5760=Euler phi(13 primorial) *)
Prepend[Select[
   Table[Flatten[Position[Table[EulerPhi[n], {n, 1, 30030}], m]], {m,
     2, 500, 2}], Length[#] == 2 &][[All, 1]], 1]

Extensions

Edited by N. J. A. Sloane, Apr 22 2016 at the suggestion of Franklin T. Adams-Watters.