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 A294712 Numbers that are the sum of three squares (square 0 allowed) in exactly nine ways. 2
 425, 521, 545, 569, 614, 650, 701, 725, 729, 774, 809, 810, 845, 857, 953, 974, 989, 990, 1053, 1062, 1070, 1074, 1091, 1118, 1134, 1139, 1166, 1179, 1217, 1249, 1251, 1262, 1266, 1277, 1298, 1310, 1418, 1446, 1458, 1470, 1525, 1541, 1546, 1571, 1594, 1611 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These are the numbers for which A000164(a(n)) = 9. 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)). This sequence is a proper subsequence of A000378. LINKS Robert Price, Table of n, a(n) for n = 1..1105 EXAMPLE 545 = 8^2 + 15^2 + 16^2 = 0^2 + 16^2 + 17^2 = 10^2 + 11^2 + 18^2 = 5^2 + 14^2 + 18^2 = 8^2 + 9^2 + 20^2 = 1^2 + 12^2 + 20^2 = 2^2 + 10^2 + 21^2 = 5^2 + 6^2 + 22^2 = 0^2 + 4^2 + 23^2. - Robert Israel, Nov 08 2017 MAPLE N:= 10000: # to get all terms <= N V:= Array(0..N): for i from 0 to isqrt(N) do for j from 0 to i while i^2 + j^2 <= N do for k from 0 to j while i^2 + j^2 + k^2 <= N do t:= i^2 + j^2 + k^2; V[t]:= V[t]+1; od od od: select(t -> V[t] = 9, [\$1..N]); # Robert Israel, Nov 08 2017 MATHEMATICA Select[Range[0, 1000], Length[PowersRepresentations[#, 3, 2]] == 9 &] CROSSREFS Cf. A000164, A005875, A000378, A094942, A224442, A224443, A294577, A294594, A294595, A294710, A294711. Sequence in context: A250342 A232359 A294714 * A160098 A349940 A203343 Adjacent sequences: A294709 A294710 A294711 * A294713 A294714 A294715 KEYWORD nonn AUTHOR Robert Price, Nov 07 2017 EXTENSIONS Updated Mathematica program to Version 11. by Robert Price, Nov 01 2019 STATUS approved

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Last modified November 29 16:16 EST 2023. Contains 367445 sequences. (Running on oeis4.)