A330069 Numbers k such that Sum_{i=1..k} i^A000010(k) == -2 (mod k).

1, 4, 60, 1716, 3444, 132396, 4428816612, 48846257124

Offset: 1

Author

José María Grau Ribas, Nov 30 2019

Keywords

• nonn
• hard
• more

Comments

Apparently includes the sequence 2*A007850.

Additional terms include 4428816612, 48846257124, 865498410347676, 29474266940021148, 1101686782618260636, 488394001964999430175732692, 1108159829234141602577157118356, 3821334362841015969111519832677012.

a(9) > 10^13. - Giovanni Resta, Feb 27 2020

Crossrefs

Cf. A000010, A054377, A007850, A330068.

Programs

Mathematica

G[n_, k_] := G[n, k] = Mod[Sum[PowerMod[i, k, n], {i, 1, n}], n];
Select[Range[2000], G[#, EulerPhi[#]] == n-2 &]
fa=FactorInteger;
se[n_, k_] := Select[Transpose[fa[n]][[1]], IntegerQ[k/(# - 1)] &];
sumlis[li_] := Sum[li[[i]], {i, 1, Length[li]}]
Table[If[Mod[-n/se[n, EulerPhi[n]] // sumlis, n] == n-2, n], {n, 1,
   1000000}] // Union

PARI

isok(n) = sumdiv(n, d, eulerphi(n/d) * Mod(d, n)^eulerphi(n)) == -2; \\ Daniel Suteu, Jan 13 2020

Extensions

a(7)-a(8) from Giovanni Resta, Feb 27 2020