Nonsquare numbers n for which S000581(n) = 1.
2, 5, 8, 13, 15, 22, 24, 26, 31, 37, 40, 46, 50, 55, 61, 70, 74, 76, 82, 94, 99, 106, 115, 120, 127, 133, 136, 142, 145, 154, 159, 166, 170, 178, 184, 202, 205, 219, 221, 235, 246, 250, 253, 265, 268, 274, 295, 298, 301, 310, 316, 319, 325, 328, 334, 340
1
This sequence is conjectured to be finite with the last term being 78754.
T. D. Noe, Plot of 198 terms
T. D. Noe, Table of 198 terms
(Mma) lim = 10000; ps = Join[{0}, Prime[Range[PrimePi[lim]]]]; sq = Range[0, Sqrt[lim]]^2; s = Select[Flatten[Table[i + j, {i, ps}, {j, sq}]], # <= lim &]; z = Complement[Range[lim], Union[s]]; za = Table[{i, 0}, {i, z}]; t = Transpose[Sort[Join[za, Tally[s]]]][[2]]; t3 = Flatten[Position[t, 1] - 1]; Select[t3, ! IntegerQ[Sqrt[#]] &]
Cf. S000581.
nonn
T. D. Noe, Apr 21 2015