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A025358 Numbers that are the sum of 4 nonzero squares in exactly 2 ways. 1
31, 34, 36, 37, 39, 43, 45, 47, 49, 50, 54, 57, 61, 68, 69, 71, 74, 77, 81, 83, 86, 94, 107, 113, 116, 131, 136, 144, 149, 200, 216, 272, 296, 344, 376, 464, 544, 576, 800, 864, 1088, 1184, 1376, 1504, 1856, 2176, 2304, 3200, 3456, 4352, 4736, 5504, 6016, 7424 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: the even members of this sequence are all numbers of the form

k*4^m for k in [9,17,29], m>= 1, or k*4^m for k in [34, 50, 54, 74, 86, 94], m>=0. - Robert Israel, Nov 03 2017

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..77 (first 71 terms from Robert Price)

Eric Weisstein's World of Mathematics, Square Number

Index entries for sequences related to sums of squares

FORMULA

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

MAPLE

N:= 10000: # to get all terms <= N

T:= Vector(N):

for a from 1 to floor(sqrt(N/4)) do

    for b from a to floor(sqrt((N-a^2)/3)) do

      for c from b to floor(sqrt((N-a^2-b^2)/2)) do

        for d from c to floor(sqrt(N-a^2-b^2-c^2)) do

          m:= a^2+b^2+c^2+d^2;

          T[m]:= T[m]+1;

od od od od:

select(i -> T[i] = 2, [$1..N]); # Robert Israel, Nov 03 2017

MATHEMATICA

M = 1000;

Clear[T]; T[_] = 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;

        T[m] = T[m] + 1;

]]]];

Select[Range[M], T[#] == 2&] (* Jean-Fran├žois Alcover, Mar 22 2019, after Robert Israel *)

CROSSREFS

Cf. A025367 (at least 2 ways).

Sequence in context: A041479 A194380 A269267 * A095473 A095467 A095461

Adjacent sequences:  A025355 A025356 A025357 * A025359 A025360 A025361

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)