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COMMENTS
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Apparently includes the sequence 2*A007850.
Additional terms include 4428816612, 48846257124, 865498410347676, 29474266940021148, 1101686782618260636, 488394001964999430175732692, 1108159829234141602577157118356, 3821334362841015969111519832677012.
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MATHEMATICA
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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
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