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

1,1

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.

Mathematica

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

Crossrefs

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

Sequence in context: A058027 A128661 A175339 * A009461 A143630 A342732

Adjacent sequences: A361966 A361967 A361968 * A361970 A361971 A361972

Keyword

nonn

Author

Amiram Eldar, Apr 01 2023

Status

approved