A361967 Number of numbers k such that uphi(k) = n, where uphi is the unitary totient function (A047994).

2, 2, 1, 2, 0, 3, 1, 4, 0, 2, 0, 5, 0, 1, 1, 2, 0, 3, 0, 2, 0, 2, 0, 8, 0, 2, 0, 3, 0, 4, 1, 4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 3, 0, 2, 0, 2, 0, 11, 0, 0, 0, 2, 0, 1, 0, 4, 0, 2, 0, 8, 0, 1, 1, 2, 0, 3, 0, 0, 0, 3, 0, 11, 0, 0, 0, 0, 0, 3, 0, 8, 0, 2, 0, 5, 0, 0, 0

Offset: 1

Author

Amiram Eldar, Apr 01 2023

Keywords

• nonn

Links

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

Crossrefs

Row lengths of A361966.

The unitary version of A014197.

Cf. A047994, A135347, A327837, A347771 (positions of 0's), A361966, A361968 (indices of records), A361969 (positions of 1's), A361970, A361971 (record values).

Programs

Mathematica

a[n_] := Length[invUPhi[n]]; Array[a, 100] (* using the function invUPhi from A361966 *)

Formula

a(A347771(n)) = 0.

a(A361969(n)) = 1.

a(A361970(n)) = n.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A327837. - Amiram Eldar, Dec 24 2024