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A025367 Numbers that are the sum of 4 nonzero squares in 2 or more ways. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Mar 22 2019, after Robert Israel *)

CROSSREFS

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

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Last modified January 19 04:09 EST 2020. Contains 331031 sequences. (Running on oeis4.)