Numbers that cannot be written as the sum of a squarefree number and a prime squared.
1, 2, 3, 4, 8, 13, 29, 49, 53, 85, 121, 125, 129, 157, 173, 193, 229, 249, 265, 293, 301, 329, 337, 365, 373, 409, 429, 445, 481, 517, 529, 533, 553, 589, 609, 625, 629, 641, 661, 697, 729, 733, 769, 805, 829, 837, 841, 845, 849, 877, 913, 929, 949, 965
1
Some numbers of the form 4*k+1 are representable.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Adrian Dudek and David J. Platt, On a theorem of Erdos in additive number theory, arXiv 1510.03677 (Apr 14 2015)
(Mma) nn = 1000; sqFree = Select[Range[nn], SquareFreeQ]; prime2 = Prime[Range[PrimePi[Sqrt[nn]]]]^2; Complement[Range[nn], Union[Select[Flatten[Table[a + b, {a, sqFree}, {b, prime2}]], # <= nn &]]]
Cf. S000637.
nonn
T. D. Noe, May 15 2015