A348058 a(n) = Min {k > n : A235137(k) == n (mod k)}, or -1 if no such minimum exists.

2, 3, 10, 5, 14, 7, 15, 16, 22, 11, 21, 13, 114, 156, 34, 17, 38, 19, 33, 25, 45, 23, 35, 80, 186, 228, 58, 29, 30, 31, 51, 64, 63, 76, 57, 37, 258, 2244, 55, 41, 86, 43, 69, 104, 94, 47, 65, 160, 1518, 372, 106, 53, 354, 81, 87, 624, 99, 59, 77, 61, 402

Offset: 1

Author

José María Grau Ribas, Sep 26 2021

Keywords

• nonn

Comments

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

If a(673) > 0 then a(673) > 10^10.

Links

• José María Grau Ribas, Table of n, a(n) for n = 1..672

Crossrefs

Cf. A235137, A348059.

Programs

Mathematica

Giuga1[mu_][n_] := Giuga1[mu][n] =
Mod[Sum[PowerMod[i, EulerPhi[n], n], {i, 1, n}] - mu, n] == 0;
A348058[n_] := A348058[n] =
{Clear[ww];  Do[If[Giuga1[n][i], ww = i; Break[]], {i, n + 1, 20000000}]; ww}[[1]];
Table[A348058[n],{n,61}]

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