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

1,1

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

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, 408}]

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, A348059.

Sequence in context: A230625 A048985 A337183 * A112417 A139693 A182076

Adjacent sequences: A348055 A348056 A348057 * A348059 A348060 A348061

Keyword

nonn

Author

José María Grau Ribas, Sep 26 2021

Status

approved