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

1,3

Links

Table of n, a(n) for n=1..86.

Example

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}.

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 *)

Crossrefs

Cf. A027750, A169580, A330893

Sequence in context: A270488 A083898 A078314 * A068322 A340967 A230243

Adjacent sequences: A330891 A330892 A330893 * A330895 A330896 A330897

Keyword

nonn

Author

Michel Lagneau, May 01 2020

Status

approved