A348059 a(n) = Min {k > n : A235137(k) == -n (mod k)}, or -1 if no such minimum exists.

2, 4, 9, 8, 6, 180, 10, 15, 14, 12, 121, 35, 22, 20, 18, 32, 289, 28, 34, 24, 38, 57, 529, 45, 46, 44, 81, 40, 546, 36, 58, 64, 62, 93, 50, 56, 210, 68, 74, 48, 42, 76, 82, 123, 54, 129, 510, 117, 94, 92, 3376098, 88, 690, 329, 106, 80, 2898, 265, 70, 72, 66

Offset: 1

Author

José María Grau Ribas, Sep 26 2021

Keywords

• nonn

Comments

Conjecture: For all n, a(n) > 0.

Crossrefs

Cf. A235137, A348058.

Programs

Mathematica

Giuga1[mu_][n_] := Giuga1[mu][n] =
Mod[Sum[PowerMod[i, EulerPhi[n], n], {i, 1, n}] + mu, n] == 0;
A348059[n_] := A348059[n] =
{Clear[ww];Do[If[Giuga1[n][i], ww = i; Break[]], {i, n + 1, 20000000}]; ww} [[1]];
Table[A348059[n],{n,49}]

PARI

a(n) = my(k=n+1); while (sum(i=1, k , Mod(i, k)^eulerphi(k)) != -n, k++); k; \\ Michel Marcus, Sep 28 2021