Number of ways that n can be written as the sum of four nonnegative squares and a prime.
0, 1, 5, 10, 11, 13, 24, 32, 27, 26, 40, 54, 55, 48, 59, 84, 80, 65, 86, 110, 110, 114, 125, 140, 140, 120, 140, 186, 180, 156, 195, 236, 218, 190, 198, 242, 277, 253, 236, 308, 305, 262, 320, 340, 326, 344, 376, 400, 409, 340, 345, 476, 453, 402, 453, 524
1
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
(Mma) nn = 10; s = Select[Sort[Flatten[Table[x^2 + y^2 + z^2 + u^2 + p, {x, 0, nn}, {y, 0, nn}, {z, 0, nn}, {u, 0, nn}, {p, Prime[Range[PrimePi[nn^2]]]}]]], # <= nn^2 &]; t = Table[0, {nn^2}]; s = Tally[s]; Do[t[[i[[1]]]] = i[[2]], {i, s}]; t
S. Chowla, The representation of a number as four squares and a prime, Acta Arithmetica, Vol. 1, No. 1, pp. 115-122.
Cf. S000125-S000136 (2 to 4 squares), A002471, A064272 (1 square).
nonn
T. D. Noe, Jul 10 2014