

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



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


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:


MATHEMATICA

Select[Range[0, 1000], Length[PowersRepresentations[#, 3, 2]] == 9 &]


CROSSREFS

Cf. A000164, A005875, A000378, A094942, A224442, A224443, A294577, A294594, A294595, A294710, A294711.


KEYWORD

nonn


AUTHOR



EXTENSIONS

Updated Mathematica program to Version 11. by Robert Price, Nov 01 2019


STATUS

approved



