A300065 Numbers k such that the number of residues modulo k of the maximum order is different from phi(phi(k)).

8, 12, 21, 24, 28, 33, 36, 42, 44, 56, 57, 63, 65, 66, 69, 72, 76, 77, 80, 84, 88, 91, 92, 93, 99, 108, 114, 117, 124, 126, 129, 130, 132, 133, 138, 141, 145, 147, 152, 154, 161, 168, 171, 172, 177, 182, 184, 185, 186, 188, 189, 195, 196, 198, 201, 207, 208, 209, 213, 216, 217, 228, 231, 234, 236, 237, 240, 248, 249, 252, 253, 258, 260, 264, 265, 266, 268, 273, 275, 276, 279, 282

Offset: 1

Author

Max Alekseyev, Feb 23 2018

Keywords

• nonn

Comments

Numbers k such that A111725(k) is not equal to A010554(k).

The ratio a(n)/n tends to 1 as n grows.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Peter J. Cameron and D. A. Preece, Primitive lambda-roots, 2014.
• T. W. Müller and J.-C. Schlage-Puchta, On the number of primitive lambda-roots, Acta Arithmetica, Vol. 115 (2004), pp. 217-223.

Crossrefs

Complement of A300064.

Union of {8} and set difference of A024619 and A300080.

Cf. A000010, A002322, A010554, A111725, A300079.

Programs

Mathematica

q[n_] := Count[(t = Table[MultiplicativeOrder[k, n], {k, Select[Range[n], CoprimeQ[n, #] &]}]), Max[t]] != EulerPhi[EulerPhi[n]]; Select[Range[300], q] (* Amiram Eldar, Oct 12 2021 *)