A361969 Numbers k with a single solution x to the equation uphi(x) = k, where uphi is the unitary totient function (A047994).

3, 7, 14, 15, 31, 54, 62, 63, 127, 154, 174, 182, 186, 234, 246, 254, 255, 294, 308, 318, 322, 364, 406, 414, 496, 510, 511, 516, 534, 558, 574, 594, 644, 666, 678, 762, 804, 806, 812, 846, 870, 948, 1022, 1023, 1026, 1036, 1074, 1098, 1146, 1148, 1164, 1204, 1246

Offset: 1

Author

Amiram Eldar, Apr 01 2023

Keywords

• nonn

Comments

Numbers k such that A361967(k) = 1.

According to Carmichael's totient function conjecture, there are no numbers with a single solution x to the corresponding equation phi(x) = k, with Euler's totient function (A000010).

A000225(m) = 2^m - 1 is a term for all m >= 2. These are the only odd terms.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Wikipedia, Carmichael's totient function conjecture.

Crossrefs

Cf. A000010, A000225, A047994, A135347, A361966, A361967, A361968, A361970, A361971.

Programs

Mathematica

Select[Range[1250], Length[invUPhi[#]] == 1 &] (* using the function invUPhi from A361966 *)