A300079 Composite numbers k such that there are exactly phi(phi(k)) residues modulo k of the maximum order.

4, 6, 9, 10, 14, 15, 16, 18, 20, 22, 25, 26, 27, 30, 32, 34, 35, 38, 39, 40, 45, 46, 48, 49, 50, 51, 52, 54, 55, 58, 60, 62, 64, 68, 70, 74, 75, 78, 81, 82, 85, 86, 87, 90, 94, 95, 96, 98, 100, 102, 104, 105, 106, 110, 111, 112, 115, 116, 118, 119, 120, 121, 122, 123, 125, 128, 134, 135, 136, 140, 142, 143, 144, 146, 148, 150, 153

Offset: 1

Author

Max Alekseyev, Feb 24 2018

Keywords

• nonn

Comments

Composite numbers k such that A111725(k) = A010554(k).

Contains as a subsequence the nontrivial prime powers (A246547) except 2^3 = 8.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A300064.

Set difference of A002808 and A300065.

Contains A300080 as a subsequence.

Cf. A000010, A002322, A010554, A111725, A246547.

Programs

Mathematica

q[n_] := Count[(t = Table[MultiplicativeOrder[k, n], {k, Select[Range[n], CoprimeQ[n, #] &]}]), Max[t]] == EulerPhi[EulerPhi[n]]; Select[Range[150], CompositeQ[#] && q[#] &] (* Amiram Eldar, Oct 12 2021 *)