Least k > 1 such that prime(n) divides k^k + (-1)^k (k-1)^(k-1).
2, 9, 8, 9, 36, 5, 3, 23, 14, 81, 45, 9, 20, 49, 14, 110, 6, 57, 26, 9, 72, 92, 120, 24, 175, 56, 9, 49, 637, 63, 88, 112, 402, 5, 144, 87, 61, 10, 332, 26, 32, 436, 105, 47, 134, 458, 16, 250, 20, 66, 144, 804, 215, 109, 495, 174, 39, 271, 4, 144, 280, 296, 291
3
This is the first-power analog of S000980. Every prime except 2 and 3 divide some term. The indices of the terms divisible by prime(n) have a periodic structure, which is shown in the next sequence.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
(Mma) t6 = {}; Do[s = Select[Range[2, p^2], Mod[PowerMod[#, #, p] + (-1)^# PowerMod[# - 1, # - 1, p], p] == 0 &, 1]; If[Length[s] > 0, AppendTo[t6, s[[1]]]], {p, Prime[Range[100]]}]; t6
Cf. S000980.
nonn
T. D. Noe, Mar 21 2017