A270266 - OEIS

%I #15 Dec 01 2024 03:57:48

%S 90,174,230,234,246,290,308,318,364,390,410,414,450,510,516,530,534,

%T 572,594,638,644,666,678,680,702,714,728,740,770,804,830,846,870,890,

%U 902,948,954,1026,1036,1074,1098,1100,1110,1130,1134,1146,1148,1164,1166,1190,1204

%N Numbers that are values of the reduced totient function (A002174) but not of the totient function (A002202).

%H Amiram Eldar, <a href="/A270266/b270266.txt">Table of n, a(n) for n = 1..10000</a>

%H William D. Banks, John B. Friedlander, Florian Luca, Francesco Pappalardi, and Igor E. Shparlinski, <a href="http://dx.doi.org/10.4064/aa122-3-1">Coincidences in the values of the Euler and Carmichael functions</a>, Acta Arithmetica 122 (2006), 207-234.

%o (PARI) isA002174(n) = if(n%2, return(n==1)); my(f=factor(n), pe); for(i=1, #f~, if(n%(f[i, 1]-1)==0, next); pe=f[i, 1]^f[i, 2]; forstep(q=2*pe+1, n+1, 2*pe, if(n%(q-1)==0 && isprime(q), next(2))); return(0)); 1 \\ _Charles R Greathouse IV_ at A002174

%o is(n) = !istotient(n) && isA002174(n); \\ _Amiram Eldar_, Dec 01 2024

%Y Cf. A000010, A002202.

%Y Cf. A002322, A002174.

%Y Cf. A270265.

%K nonn

%O 1,1

%A _Michel Marcus_, Mar 14 2016