

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
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OFFSET

1,1


COMMENTS

These are the numbers for which A000164(a(n)) = 9.
a(n) is the nth 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 A203343 A207233
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



