A025367 Numbers that are the sum of 4 nonzero squares in 2 or more ways.

28, 31, 34, 36, 37, 39, 42, 43, 45, 47, 49, 50, 52, 54, 55, 57, 58, 60, 61, 63, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 102, 103, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sums of squares

Formula

{n: A025428(n) >= 2}. - R. J. Mathar, Jun 15 2018

Maple

N:= 1000: # to get all terms <= N
V:= Vector(N):
for x from 1 while x^2 +3 <= N do
for y from 1 to x while x^2 + y^2 + 2 <= N do
  for z from 1 to y while x^2 + y^2 + z^2 + 1 <= N do
    for w from 1 to z while x^2 + y^2 + z^2 + w^2 <= N do
       t:= x^2 + y^2 + z^2 + w^2;
       V[t]:= V[t]+1;
od od od od:
select(t -> V[t] >= 2, [$1..N]); # Robert Israel, Jul 05 2017

Mathematica

Select[Range@ 200, 2 == Length@ Quiet@ IntegerPartitions[#, {4}, Range[Sqrt@ #]^2, 2] &] (* Giovanni Resta, Jul 05 2017 *)
M = 1000;
Clear[V]; V[_] = 0;
For[a = 1, a <= Floor[Sqrt[M/4]], a++,
  For[b = a, b <= Floor[Sqrt[(M - a^2)/3]], b++,
    For[c = b, c <= Floor[Sqrt[(M - a^2 - b^2)/2]], c++,
      For[d = c, d <= Floor[Sqrt[M - a^2 - b^2 - c^2]], d++,
        m = a^2 + b^2 + c^2 + d^2;
        V[m] = V[m] + 1;
]]]];
Select[Range[M], V[#] >= 2&] (* Jean-François Alcover, Mar 22 2019, after Robert Israel *)

Crossrefs

Cf. A000414, A024796, A025358, A025368, A025406, A344795.

Sequence in context: A067913 A116566 A057483 * A121018 A232727 A232766

Adjacent sequences: A025364 A025365 A025366 * A025368 A025369 A025370

Keyword

nonn

Author

David W. Wilson

Status

approved