A330894 Numbers of Pythagorean quadruples contained in the divisors of A330893(n).

1, 1, 2, 2, 2, 1, 3, 1, 3, 2, 4, 3, 2, 2, 1, 4, 1, 2, 3, 2, 7, 4, 2, 2, 8, 2, 1, 4, 4, 2, 3, 7, 3, 2, 5, 2, 2, 4, 6, 2, 5, 2, 11, 6, 4, 1, 4, 1, 6, 2, 4, 12, 2, 5, 1, 4, 6, 4, 2, 5, 6, 4, 1, 2, 3, 4, 17, 6, 2, 3, 6, 1, 5, 6, 1, 3, 4, 6, 6, 13, 1, 2, 4, 8, 4, 4

Offset: 1

Author

Michel Lagneau, May 01 2020

Keywords

• nonn

Examples

			a(7) = 3 because A330893(7)=168, and the set of divisors of 168: {1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168} contains three Pythagorean quadruples {2, 3, 6, 7}, {4, 6, 12, 14} and {8, 12, 24, 28}.
		

Crossrefs

Cf. A027750, A169580, A330893

Programs

Maple

with(numtheory):
for n from 3 to 1700 do :
   d:=divisors(n):n0:=nops(d):it:=0:
    for i from 1 to n0-3 do:
     for j from i+1 to n0-2 do :
      for k from j+1 to n0-1 do:
      for m from k+1 to n0 do:
       if d[i]^2 + d[j]^2 + d[k]^2 = d[m]^2
        then
        it:=it+1:
        else
       fi:
      od:
     od:
    od:
    od:
    if it>0 then
    printf(`%d, `,it):
    else fi:
   od:

Mathematica

nq[n_] := If[Mod[n, 6] > 0, 0, Block[{t, u, v, c = 0, d = Divisors[n], m}, m = Length@ d; Do[t = d[[i]]^2 + d[[j]]^2; Do[u = t + d[[h]]^2; If[u > n^2, Break[]]; If[Mod[n^2, u] == 0 && IntegerQ[v = Sqrt@ u] && Mod[n, v] == 0, c++], {h, j+1, m-1}], {i, m-3}, {j, i+1, m - 2}]; c]]; Select[Array[nq, 1638], # > 0 &] (* Giovanni Resta, May 04 2020 *)