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A339273
Sums of two nonzero even squares.
0
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
1,1
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).
EXAMPLE
20 is in the sequence since it is the sum of two nonzero even squares, 2^2 + 4^2 = 4 + 16 = 20.
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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Dec 24 2020
STATUS
approved