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

1,1

Comments

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

Links

Table of n, a(n) for n=1..61.

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}]

Prog

(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

Crossrefs

Cf. A235137, A348058.

Sequence in context: A241473 A055858 A141389 * A076125 A011033 A179219

Adjacent sequences: A348056 A348057 A348058 * A348060 A348061 A348062

Keyword

nonn

Author

José María Grau Ribas, Sep 26 2021

Status

approved