A345674 Euler totient function phi(n) - number of primitive roots modulo n.

0, 0, 1, 1, 2, 1, 4, 4, 4, 2, 6, 4, 8, 4, 8, 8, 8, 4, 12, 8, 12, 6, 12, 8, 12, 8, 12, 12, 16, 8, 22, 16, 20, 8, 24, 12, 24, 12, 24, 16, 24, 12, 30, 20, 24, 12, 24, 16, 30, 12, 32, 24, 28, 12, 40, 24, 36, 16, 30, 16, 44, 22, 36, 32, 48, 20, 46, 32, 44, 24

Offset

1,5

Links

Table of n, a(n) for n=1..70.

Formula

a(n) = A000010(n) - A046144(n).

Maple

a:= proc(n) uses numtheory; `if`(n=1, 0, (p->
      p-add(`if`(order(i, n)=p, 1, 0), i=0..n-1))(phi(n)))
    end:
seq(a(n), n=1..70);  # Alois P. Heinz, Jun 22 2021

Mathematica

a[n_] := (e = EulerPhi[n]) - If[n == 1 || IntegerQ @ PrimitiveRoot[n], EulerPhi[e], 0]; Array[a, 100] (* Amiram Eldar, Jun 23 2021 *)

Crossrefs

Cf. A000010, A046144.

Sequence in context: A110316 A111975 A117250 * A296337 A308432 A136692

Adjacent sequences: A345671 A345672 A345673 * A345675 A345676 A345677

Keyword

nonn

Author

Robert Hutchins, Jun 22 2021

Status

approved