## S001065

Primitive Pythagorean septuples (a, b, c, d, e, f, g) sorted.

1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 3, 5, 1, 1, 1, 1, 4, 4, 6, 1, 1, 1, 2, 2, 5, 6, 1, 2, 2, 3, 3, 3, 6, 1, 1, 1, 1, 3, 6, 7, 1, 1, 2, 3, 3, 5, 7, 2, 3, 3, 3, 3, 3, 7, 1, 1, 1, 3, 4, 6, 8, 1, 2, 3, 3, 4, 5, 8, 1, 1, 1, 2, 5, 7, 9, 1, 1, 2, 5, 5, 5, 9

1

Septuples such that g^2 = f^2 + e^2 + d^2 + c^2 + b^2 + a^2. There are only a finite number of cases that sum to a given g^2.

T. D. Noe, Plot of 1106 septuples

T. D. Noe, Table of 1106 septuples

(Mma) a =.; b =.; c =.; d =.; e =.; f =.; t = {}; terms = 0; g = 0; While[terms < 100, g++; sol = Solve[a^2 + b^2 + c^2 + d^2 + e^2 + f^2 == g^2 && 0 < a <= b <= c <= d <= e <= f <= g, {a, b, c, d, e, f}, Integers]; If[Length[sol] > 0, t8 = Table[Table[sol[[i]][[j, 2]], {j, 6}], {i, Length[sol]}]; sol = Select[t8, GCD @@ # == 1 &]; If[Length[sol] > 0, sol = Transpose[Join[Transpose[sol], {Table[g, {Length[sol]}]}]]; t = Join[t, Sort[sol]]; terms = terms + Length[sol]]]]; t

Cf.S001069.

nonn,tabl

T. D. Noe, Aug 10 2017