A122904 Numbers m such that in Z/mZ the number of squares is strictly less than the number of invertible elements.

5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 88, 89, 91, 92, 93, 95, 96, 97, 99, 100

Offset: 1

Author

Max Alekseyev, Sep 18 2006

Keywords

• nonn

Comments

Numbers m such that A000224(m) < A000010(m).

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A000224, A122903, A122905, A122906, A122907.

Programs

Mathematica

Select[Range@100, Length@Union@Mod[Range[#]^2, #] < EulerPhi[#] &] (* Ivan Neretin, Dec 14 2016 *)
f1[p_, e_] := Floor[p^(e+1)/(2p + 2)] + 1; f1[2, e_] := Floor[2^e/6] + 2; f[p_, e_] := f1[p, e]/((p-1) * p^(e-1)); q[1] = False; q[k_] := Times @@ f @@@ FactorInteger[k] < 1; Select[Range[100], q] (* Amiram Eldar, Nov 11 2024 *)