A339273 Sums of two nonzero even squares.

8, 20, 32, 40, 52, 68, 72, 80, 100, 104, 116, 128, 136, 148, 160, 164, 180, 200, 208, 212, 232, 244, 260, 272, 288, 292, 296, 320, 328, 340, 356, 360, 388, 392, 400, 404, 416, 424, 436, 452, 464, 468, 488, 500, 512, 520, 544, 548, 580, 584, 592, 596, 612, 628, 640, 648, 656

Offset: 1

Author

Wesley Ivan Hurt, Dec 24 2020

Keywords

• nonn
• easy

Examples

			20 is in the sequence since it is the sum of two nonzero even squares, 2^2 + 4^2 = 4 + 16 = 20.
		

Crossrefs

Cf. A000404, A010052, A057653, A097269.

Programs

Mathematica

Table[If[Sum[Mod[i + 1, 2] Mod[n - i + 1, 2] (Floor[Sqrt[i]] - Floor[Sqrt[i - 1]]) (Floor[Sqrt[n - i]] - Floor[Sqrt[n - i - 1]]), {i, Floor[n/2]}] > 0, n, {}], {n, 700}] // Flatten

Formula

a(n) = 4*A000404(n).

Characteristic function: sign(Sum_{k=1..floor(n/2)} ((k+1) mod 2) * ((n-k+1) mod 2) * c(k) * c(n-k)), where c is the characteristic function of squares (A010052).