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A294712 Numbers that are the sum of three squares (square 0 allowed) in exactly nine ways.

%I A294712 #17 Nov 01 2019 22:21:41
%S A294712 425,521,545,569,614,650,701,725,729,774,809,810,845,857,953,974,989,
%T A294712 990,1053,1062,1070,1074,1091,1118,1134,1139,1166,1179,1217,1249,1251,
%U A294712 1262,1266,1277,1298,1310,1418,1446,1458,1470,1525,1541,1546,1571,1594,1611
%N A294712 Numbers that are the sum of three squares (square 0 allowed) in exactly nine ways.
%C A294712 These are the numbers for which A000164(a(n)) = 9.
%C A294712 a(n) is the n-th largest number which has a representation as a sum of three integer squares (square 0 allowed), in exactly nine ways, if neither the order of terms nor the signs of the numbers to be squared are taken into account. The multiplicity of a(n) with order and signs taken into account is A005875(a(n)).
%C A294712 This sequence is a proper subsequence of A000378.
%H A294712 Robert Price, <a href="/A294712/b294712.txt">Table of n, a(n) for n = 1..1105</a>
%e A294712 545 =  8^2 + 15^2 + 16^2
%e A294712     =  0^2 + 16^2 + 17^2
%e A294712     = 10^2 + 11^2 + 18^2
%e A294712     =  5^2 + 14^2 + 18^2
%e A294712     =  8^2 +  9^2 + 20^2
%e A294712     =  1^2 + 12^2 + 20^2
%e A294712     =  2^2 + 10^2 + 21^2
%e A294712     =  5^2 +  6^2 + 22^2
%e A294712     =  0^2 +  4^2 + 23^2. - _Robert Israel_, Nov 08 2017
%p A294712 N:= 10000: # to get all terms <= N
%p A294712 V:= Array(0..N):
%p A294712 for i from 0 to isqrt(N) do
%p A294712   for j from 0 to i while i^2 + j^2 <= N do
%p A294712     for k from 0 to j while i^2 + j^2 + k^2 <= N do
%p A294712       t:= i^2 + j^2 + k^2;
%p A294712       V[t]:= V[t]+1;
%p A294712 od od od:
%p A294712 select(t -> V[t] = 9, [$1..N]); # _Robert Israel_, Nov 08 2017
%t A294712 Select[Range[0, 1000], Length[PowersRepresentations[#, 3, 2]] == 9 &]
%Y A294712 Cf. A000164, A005875, A000378, A094942, A224442, A224443, A294577, A294594, A294595, A294710, A294711.
%K A294712 nonn
%O A294712 1,1
%A A294712 _Robert Price_, Nov 07 2017
%E A294712 Updated Mathematica program to Version 11. by _Robert Price_, Nov 01 2019