A394430 - OEIS

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.

%I #6 Mar 24 2026 22:29:16

%S 1,8,24,32,44,48,56,64,80,84,92,104,116,120,128,132,140,144,160,164,

%T 168,176,184,200,204,208,212,216,220,224,252,260,264,288,296,300,320,

%U 324,328,332,344,356,360,368,380,384,392,416,424,440,444,452,464,468,476,480,492,504,512,524

%N 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.

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

%H Miles Englezou, <a href="/A394430/b394430.txt">Table of n, a(n) for n = 1..10000</a>

%H Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).

%e 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.

%e 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.

%o (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

%Y Cf. A000010, A002202.

%K nonn

%O 1,2

%A _Miles Englezou_, Mar 20 2026