Number of ways that n can be written as the sum of four positive squares and a prime.
0, 0, 0, 0, 0, 1, 1, 0, 5, 4, 1, 10, 6, 8, 15, 4, 23, 21, 5, 32, 24, 22, 34, 28, 46, 40, 38, 46, 53, 60, 40, 72, 84, 56, 78, 82, 78, 101, 90, 80, 142, 110, 71, 156, 120, 116, 165, 128, 173, 168, 129, 174, 202, 174, 159, 228, 224, 188, 230, 230, 226, 280, 234
1
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
S. Chowla, The representation of a number as four squares and a prime, Acta Arithmetica, Vol. 1, No. 1, pp. 115-122.
(Mma) nn = 10; s = Select[Sort[Flatten[Table[x^2 + y^2 + z^2 + u^2 + p, {x, nn}, {y, nn}, {z, nn}, {u, 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
Cf. S000125-S000136 (2 to 4 squares), A002471, A064272 (1 square).
nonn
T. D. Noe, Jul 10 2014