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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 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-François 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 STATUS approved

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