A025323 -id:A025323 - cp's OEIS frontend

A025324 Numbers that are the sum of 3 nonzero squares in exactly 4 ways.

129, 134, 146, 153, 161, 171, 189, 198, 201, 234, 243, 246, 249, 251, 254, 257, 261, 270, 278, 285, 290, 293, 294, 299, 339, 353, 362, 363, 365, 371, 378, 387, 390, 393, 395, 405, 406, 409, 411, 417, 429, 451, 454, 465, 467, 469, 473, 477, 485, 501, 502, 510, 514, 516

Offset: 1

David W. Wilson

nonn

			299 is a term because 299 = 1^2 + 3^2 + 17^2 = 3^2 + 11^2 + 13^2 = 5^2 + 7^2 + 15^2 = 7^2 + 9^2 + 13^2 and there are no more such sums of four nonzero squares giving 182. - _David A. Corneth_, Feb 13 2019

David A. Corneth, Table of n, a(n) for n = 1..1705 (first 593 terms from Robert Price, terms <= 2*10^6)
David A. Corneth, Terms below (inclusive) 2*10^6 with the sums of squares
David A. Corneth, PARI program
Eric Weisstein's World of Mathematics, Square Number.
Index entries for sequences related to sums of squares

Cf. A024796, A025427, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338.

Select[Range@ 600, Length@ # == 4 &@ DeleteCases[PowersRepresentations[#, 3, 2], ?(AnyTrue[#, # == 0 &] &)] &] (* _Michael De Vlieger, Feb 13 2019 *)

\\ See Corneth link \\ David A. Corneth, Feb 13 2019

A025325 Numbers that are the sum of 3 nonzero squares in exactly 5 ways.

Original entry on oeis.org

194, 206, 230, 266, 269, 281, 350, 354, 381, 386, 389, 398, 401, 402, 413, 414, 419, 437, 449, 450, 470, 474, 482, 491, 525, 539, 554, 563, 579, 582, 585, 590, 601, 611, 630, 635, 638, 642, 646, 722, 769, 776, 781, 786, 819, 824, 829, 830, 834, 851, 867, 874, 878, 886

Offset: 1

David W. Wilson

nonn

Robert Price, Table of n, a(n) for n = 1..441
Index entries for sequences related to sums of squares

Cf. A024796, A025427, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338.

A025326 Numbers that are the sum of 3 nonzero squares in exactly 6 ways.

Original entry on oeis.org

209, 297, 306, 314, 321, 326, 329, 342, 425, 426, 434, 441, 458, 459, 489, 497, 513, 530, 531, 534, 542, 546, 558, 561, 593, 602, 605, 633, 649, 650, 657, 659, 662, 665, 674, 675, 678, 681, 693, 698, 699, 705, 706, 713, 714, 725, 737, 738, 741, 746, 747, 750, 755, 758

Offset: 1

David W. Wilson

nonn

Robert Price, Table of n, a(n) for n = 1..707
Index entries for sequences related to sums of squares

Cf. A024796, A025427, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338.

A025327 Numbers that are the sum of 3 nonzero squares in exactly 7 ways.

Original entry on oeis.org

341, 369, 461, 494, 506, 509, 545, 549, 581, 641, 654, 666, 677, 726, 731, 797, 806, 818, 821, 833, 882, 891, 893, 894, 899, 906, 934, 954, 978, 981, 998, 1011, 1017, 1019, 1050, 1067, 1069, 1086, 1094, 1098, 1101, 1133, 1158, 1194, 1211, 1233, 1294, 1331, 1346

Offset: 1

David W. Wilson

nonn

Robert Price, Table of n, a(n) for n = 1..422
Index entries for sequences related to sums of squares

Cf. A024796, A025427, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338.

A025328 Numbers that are the sum of 3 nonzero squares in exactly 8 ways.

Original entry on oeis.org

374, 446, 486, 521, 566, 569, 621, 629, 686, 701, 710, 729, 749, 770, 789, 809, 810, 825, 849, 857, 869, 902, 945, 953, 969, 971, 1014, 1022, 1029, 1053, 1085, 1125, 1146, 1174, 1217, 1221, 1241, 1242, 1245, 1249, 1250, 1253, 1254, 1259, 1269, 1277, 1334, 1379

Offset: 1

David W. Wilson

nonn

Robert Price, Table of n, a(n) for n = 1..649
Index entries for sequences related to sums of squares

Cf. A024796, A025427, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338.

A025329 Numbers that are the sum of 3 nonzero squares in exactly 9 ways.

Original entry on oeis.org

614, 626, 689, 774, 914, 929, 974, 989, 990, 1025, 1062, 1070, 1074, 1091, 1097, 1118, 1134, 1139, 1166, 1179, 1193, 1205, 1229, 1251, 1262, 1266, 1289, 1298, 1305, 1310, 1325, 1409, 1433, 1446, 1470, 1541, 1571, 1611, 1637, 1638, 1745, 1754, 1821, 1834

Offset: 1

David W. Wilson

nonn

Robert Price, Table of n, a(n) for n = 1..400
Index entries for sequences related to sums of squares

Cf. A024796, A025427, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338.

A025330 Numbers that are the sum of 3 nonzero squares in exactly 10 ways.

Original entry on oeis.org

594, 734, 761, 794, 801, 846, 881, 909, 926, 965, 986, 1001, 1026, 1041, 1089, 1130, 1190, 1209, 1214, 1226, 1265, 1274, 1322, 1326, 1329, 1341, 1370, 1382, 1386, 1505, 1509, 1553, 1557, 1581, 1586, 1613, 1625, 1658, 1689, 1691, 1709, 1713, 1725, 1739

Offset: 1

David W. Wilson

nonn

Robert Price, Table of n, a(n) for n = 1..592
Index entries for sequences related to sums of squares

Cf. A024796, A025427, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338.

A025397 Numbers that are the sum of 3 positive cubes in exactly 3 ways.

Original entry on oeis.org

5104, 9729, 12104, 12221, 12384, 14175, 17604, 17928, 19034, 20691, 21412, 21888, 24480, 28792, 29457, 30528, 31221, 32850, 34497, 35216, 36288, 38259, 39339, 39376, 40060, 40097, 40832, 40851, 41033, 41040, 41364, 41966, 42056, 42687, 43408, 45144

Offset: 1

David W. Wilson

nonn

Donovan Johnson, Table of n, a(n) for n = 1..10000

Cf. A008917, A025323, A025396, A025398, A025405, A025456, A343969, A344240, A344804.

N:= 10^5: # to get all terms <= N
Reps:= Matrix(N,3,(i,j) -> {}):
for i from 1 to floor(N^(1/3)) do
  Reps[i^3,1]:= {[i]}
od:
for j from 2 to 3 do
for i from 1 to floor(N^(1/3)) do
  for x from i^3+1 to N do
    Reps[x,j]:= Reps[x,j] union
      map(t -> if t[-1] <= i then [op(t),i] fi, Reps[x-i^3,j-1]);
  od
od
od:
select(t -> nops(Reps[t,3])=3, [$1..N]); # Robert Israel, Aug 28 2015

Reap[ For[ n = 1, n <= 50000, n++, pr = Select[ PowersRepresentations[n, 3, 3], Times @@ # != 0 &]; If[pr != {} && Length[pr] == 3, Print[n, pr]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jul 31 2013 *)

is(n)=k=ceil((n-2)^(1/3)); d=0; for(a=1, k, for(b=a, k, for(c=b, k, if(a^3+b^3+c^3==n, d++)))); d
n=3; while(n<50000, if(is(n)==3, print1(n, ", ")); n++) \\ Derek Orr, Aug 27 2015

n such that A025456(n) = 3. - Robert Israel, Aug 28 2015

cp's OEIS Frontend

A025324 Numbers that are the sum of 3 nonzero squares in exactly 4 ways.

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A025325 Numbers that are the sum of 3 nonzero squares in exactly 5 ways.

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A025326 Numbers that are the sum of 3 nonzero squares in exactly 6 ways.

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A025327 Numbers that are the sum of 3 nonzero squares in exactly 7 ways.

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A025328 Numbers that are the sum of 3 nonzero squares in exactly 8 ways.

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A025329 Numbers that are the sum of 3 nonzero squares in exactly 9 ways.

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A025330 Numbers that are the sum of 3 nonzero squares in exactly 10 ways.

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A025397 Numbers that are the sum of 3 positive cubes in exactly 3 ways.

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