Values of k in the range of 1 < k < S000980(n)^2 such that S000980(n)^2 divides k^k + (-1)^k (k-1)^(k-1).
257, 487, 528, 815, 897, 1176, 1225, 1373, 2050, 2198, 2247, 2526, 2608, 2895, 2936, 3166, 130, 1320, 2084, 2958, 3849, 4723, 5487, 6677, 1430, 2029, 13158, 14502, 17361, 18705, 29834, 30433, 10702, 26355, 16252, 96981, 38398, 49174, 61255, 82014, 93129
1
The first array ends with 6677.
T. D. Noe, Plot of 153 arrays
T. D. Noe, Table of 153 arrays
David W. Boyd, Greg Martin, and Mark Thom, Squarefree values of trinomial discriminants, LMS J. Comput. Math. 18 (1) (2015), p. 148-169
(Mma) t3 = {}; Do[s = Select[Range[2, p^2], Mod[PowerMod[#, #, p^2] + (-1)^# PowerMod[# - 1, # - 1, p^2], p^2] == 0 &]; If[Length[s] > 0, AppendTo[t3, s]], {p, Prime[Range[PrimePi[1000]]]}]; t3
nonn,hard
T. D. Noe, Mar 18 2017