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