A274485 Least number of the form x^n + y^n that is the sum of two positive squares in exactly n ways (x, y > 0).

2, 50, 3925, 50881, 625000000, 117650, 1562500000000, 815737282, 3906250000000000, 25937425625, 9765625000000000000, 23298085126577, 24414062500000000000000, 7862651120078217664621465531250, 61035156250000000000000000, 10000000000000001, 152587890625000000000000000000

Offset

1,1

Links

Table of n, a(n) for n=1..17.

Example

a(2) = 50 because 50 = 1^2 + 7^2 = 5^2 + 5^2.
a(3) = 3925 because 3925 = 12^3 + 13^3 = 9^2 + 62^2 = 26^2 + 57^2 = 30^2 + 55^2.
a(4) = 50881 because 50881 = 4^4 + 15^4 = 16^2 + 225^2 = 65^2 + 216^2 = 120^2 + 191^2 = 159^2 + 160^2.

Mathematica

nR[n_]:= (SquaresR[2, n]+ Plus@@ Pick[{-4, 4}, IntegerQ/@ Sqrt[{n, n/2} ]])/8; a[1]=2; a[n_]:= Block[{m = 10^3, s, z}, While[{} == (s = Reap[ Do[ If[nR[z = x^n + y^n] == n, Sow@ z], {x, Floor[m^(1/n)]}, {y, Min[x, Floor[m - x^n]^(1/n)]}]][[2]]), m *= 2]; Min[s[[1]]]]; Array[a, 10] (* Giovanni Resta, Jun 27 2016 *)

Crossrefs

Sequence in context: A231043 A356611 A079198 * A210919 A210924 A355629

Adjacent sequences: A274482 A274483 A274484 * A274486 A274487 A274488

Keyword

nonn

Author

Altug Alkan, Jun 24 2016

Extensions

a(5)-a(17) from Giovanni Resta, Jun 27 2016

Status

approved