A294595 -id:A294595 - cp's OEIS frontend

A294710 Numbers that are the sum of three squares (square 0 allowed) in exactly seven ways.

306, 314, 341, 441, 450, 458, 494, 506, 581, 585, 593, 605, 654, 657, 674, 698, 706, 726, 731, 738, 746, 773, 806, 842, 850, 873, 890, 891, 893, 894, 899, 901, 905, 906, 934, 978, 985, 998, 1011, 1013, 1019, 1050, 1058, 1061, 1067, 1073, 1086, 1094, 1101

Offset: 1

Robert Price, Nov 07 2017

nonn

These are the numbers for which A000164(a(n)) = 7.
a(n) is the n-th largest number which has a representation as a sum of three integer squares (square 0 allowed), in exactly seven 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.

Robert Price, Table of n, a(n) for n = 1..988

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

Select[Range[0, 1000], Length[PowersRepresentations[#, 3, 2]] == 7 &]

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

A294711 Numbers that are the sum of three squares (square 0 allowed) in exactly eight ways.

Original entry on oeis.org

369, 374, 446, 461, 486, 509, 530, 549, 566, 621, 641, 666, 677, 686, 710, 749, 770, 789, 797, 818, 821, 825, 833, 849, 869, 882, 902, 945, 954, 962, 969, 971, 981, 1010, 1014, 1017, 1022, 1029, 1069, 1085, 1098, 1146, 1157, 1174, 1221, 1233, 1242, 1245

Offset: 1

Robert Price, Nov 07 2017

nonn

These are the numbers for which A000164(a(n)) = 8.
a(n) is the n-th largest number which has a representation as a sum of three integer squares (square 0 allowed), in exactly eight 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.

Robert Price, Table of n, a(n) for n = 1..1701

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

Select[Range[0, 1000], Length[PowersRepresentations[#, 3, 2]] == 8 &]

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

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

Original entry on oeis.org

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

Offset: 1

Robert Price, Nov 07 2017

nonn

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.

			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

Robert Price, Table of n, a(n) for n = 1..1105

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

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

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

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

A294713 Numbers that are the sum of three squares (square 0 allowed) in exactly ten ways.

Original entry on oeis.org

594, 626, 629, 734, 846, 914, 926, 929, 1001, 1026, 1041, 1097, 1125, 1190, 1193, 1209, 1214, 1229, 1241, 1265, 1289, 1326, 1329, 1382, 1386, 1409, 1433, 1490, 1505, 1509, 1521, 1530, 1581, 1637, 1689, 1691, 1713, 1725, 1730, 1739, 1749, 1754, 1770, 1778

Offset: 1

Robert Price, Nov 07 2017

nonn

These are the numbers for which A000164(a(n)) = 10.
a(n) is the n-th largest number which has a representation as a sum of three integer squares (square 0 allowed), in exactly ten 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.

Robert Price, Table of n, a(n) for n = 1..1835

Cf. A000164, A005875, A000378, A094942, A224442, A224443, A294577, A294594, A294595, A294710, A294711, A294712.

Select[Range[0, 1000], Length[PowersRepresentations[#, 3, 2]] == 10 &]

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

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A294710 Numbers that are the sum of three squares (square 0 allowed) in exactly seven ways.

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A294711 Numbers that are the sum of three squares (square 0 allowed) in exactly eight ways.

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

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A294713 Numbers that are the sum of three squares (square 0 allowed) in exactly ten ways.

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Mathematica

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