A394430 Totient numbers k for which there does not exist an m = p^e or 2*p^e, p an odd prime and e >= 1, such that phi(m) = k.

1, 8, 24, 32, 44, 48, 56, 64, 80, 84, 92, 104, 116, 120, 128, 132, 140, 144, 160, 164, 168, 176, 184, 200, 204, 208, 212, 216, 220, 224, 252, 260, 264, 288, 296, 300, 320, 324, 328, 332, 344, 356, 360, 368, 380, 384, 392, 416, 424, 440, 444, 452, 464, 468, 476, 480, 492, 504, 512, 524

Offset

1,2

Comments

Totient numbers k such that the cyclic group C_k does not appear as the group of units of a ring Z/rZ.

Links

Miles Englezou, Table of n, a(n) for n = 1..10000

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Example

8 is a term since phi(m) = 8 for m in {15, 16, 20, 24, 30} and none of these m are an odd prime power or twice an odd prime power.
24 is a term since phi(m) = 24 for m in {35, 39, 45, 52, 56, 70, 72, 78, 84, 90} and none of these m are an odd prime power or twice an odd prime power.

Prog

(PARI) isok(n) = istotient(n) && select(y -> y==[n], Set(apply(x -> znstar(x)[2], invphi(n))))==[] \\ using Max Alekseyev's invphi.gp; see link

Crossrefs

Cf. A000010, A002202.

Sequence in context: A056196 A044069 A028628 * A333427 A128690 A283078

Adjacent sequences: A394426 A394427 A394428 * A394431 A394432 A394433

Keyword

nonn

Author

Miles Englezou, Mar 20 2026

Status

approved