A300080 Numbers k that are not prime powers, and have exactly phi(phi(k)) residues modulo k of the maximum order.

6, 10, 14, 15, 18, 20, 22, 26, 30, 34, 35, 38, 39, 40, 45, 46, 48, 50, 51, 52, 54, 55, 58, 60, 62, 68, 70, 74, 75, 78, 82, 85, 86, 87, 90, 94, 95, 96, 98, 100, 102, 104, 105, 106, 110, 111, 112, 115, 116, 118, 119, 120, 122, 123, 134, 135, 136, 140, 142, 143, 144, 146, 148, 150, 153, 155, 156, 158, 159, 160, 162, 164, 165, 166

Offset: 1

Author

Max Alekseyev, Feb 24 2018

Keywords

• nonn

Comments

Numbers k with at least two distinct prime factors (A024619) such that A111725(k) = A010554(k).

Links

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

Crossrefs

Set difference of: A300064 and A000961, A300079 and A246547, A024619 and A300065.

Cf. A000010, A002322, A010554, A111725.

Programs

Mathematica

q[n_] := Count[(t = Table[MultiplicativeOrder[k, n], {k, Select[Range[n], CoprimeQ[n, #] &]}]), Max[t]] == EulerPhi[EulerPhi[n]]; Select[Range[200], PrimeNu[#] > 1 && q[#] &] (* Amiram Eldar, Oct 12 2021 *)