A274046 -id:A274046 - cp's OEIS frontend

A275154 Smallest positive integer which can be represented as the sum of distinct positive cubes in exactly n ways, or 0 if no such integer exists.

1, 216, 729, 1072, 1736, 1737, 2465, 2800, 2808, 3619, 3276, 4257, 4131, 4662, 4473, 5292, 5265, 5328, 6084, 5481, 6202, 5985, 6777, 6840, 7056, 7372, 7659, 7560, 7588, 7380, 7596, 7722, 8037, 8190, 8576, 8064, 8316, 9297, 9549, 8380, 9045, 9261, 9451, 9360, 8919, 10044, 9108

Offset: 1

Ilya Gutkovskiy, Jun 01 2017

nonn

For all k in [63159..10^9], Q(k,500) >= 2092 so Q(k, infinity) >= 2092 for k>=63159 where Q(k, u) is the number of ways to write k as a sum of distinct cubes c where c <= u^3 (see proof in Du Link). Hence, a(2091)=0. - Zhao Hui Du, Jun 22 2025

			a(4) = 1072 because 1072 = 7^3 + 9^3 = 2^3 + 4^3 + 10^3 = 1^3 + 6^3 + 7^3 + 8^3 = 1^3 + 3^3 + 4^3 + 5^3 + 7^3 + 8^3 and this is the smallest number that can be written as the sum of distinct positive cubes in 4 different ways.

David A. Corneth, Table of n, a(n) for n = 1..10000
Zhao Hui Du, Proof for the theorem related to Q(k,u)
Index entries for sequences related to sums of cubes

Cf. A003997, A097563, A274046, A279329.

A279329(a(n)) = n.

A350205 a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero tetrahedral numbers in exactly n ways, or 0 if no such integer exists.

Original entry on oeis.org

1, 35, 140, 175, 225, 290, 374, 400, 430, 455, 539, 540, 630, 655, 690, 595, 680, 760, 795, 715, 770, 865, 830, 945, 875, 980, 935, 960, 1080, 990, 970, 1075, 995, 1160, 1165, 1110, 1050, 1170, 1135, 1220, 1190, 1350, 1305, 1285, 1389, 1310, 1320, 1360, 1355, 1340

Offset: 1

Ilya Gutkovskiy, Dec 19 2021

nonn

Eric Weisstein's World of Mathematics, Tetrahedral Number

Cf. A000292, A274046, A279278, A350206.

A350196 a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero pentagonal numbers in exactly n ways, or 0 if no such integer exists.

Original entry on oeis.org

1, 35, 92, 127, 144, 214, 237, 215, 249, 250, 319, 315, 354, 355, 366, 390, 391, 432, 431, 425, 475, 448, 478, 460, 482, 483, 510, 495, 537, 531, 525, 545, 570, 560, 594, 566, 581, 582, 606, 601, 595, 618, 603, 630, 602, 625, 652, 666, 657, 641

Offset: 1

Ilya Gutkovskiy, Dec 19 2021

nonn

Eric Weisstein's World of Mathematics, Pentagonal Number

Cf. A000326, A097563, A218380, A274046, A350197, A350198, A350199.

A350197 a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero hexagonal numbers in exactly n ways, or 0 if no such integer exists.

Original entry on oeis.org

1, 66, 126, 186, 277, 305, 377, 325, 416, 371, 445, 451, 511, 496, 536, 557, 607, 575, 653, 602, 630, 641, 682, 675, 668, 701, 710, 742, 746, 760, 767, 755, 800, 761, 874, 794, 845, 806, 846, 821, 861, 881, 880, 887, 867, 905, 906, 886, 911, 900

Offset: 1

Ilya Gutkovskiy, Dec 19 2021

nonn

Eric Weisstein's World of Mathematics, Hexagonal Number

Cf. A000384, A097563, A274046, A279279, A350196, A350198, A350199.

A350198 a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero heptagonal numbers in exactly n ways, or 0 if no such integer exists.

Original entry on oeis.org

1, 81, 189, 270, 343, 342, 456, 538, 557, 531, 651, 636, 676, 658, 723, 804, 784, 777, 770, 825, 844, 865, 890, 975, 960, 941, 966, 983, 959, 1030, 1040, 1012, 1080, 1053, 1039, 1119, 1046, 1078, 1079, 1064, 1072, 1173, 1071, 1180, 1152, 1193, 1194, 1226, 1220, 1247

Offset: 1

Ilya Gutkovskiy, Dec 19 2021

nonn

Eric Weisstein's World of Mathematics, Heptagonal Number

Cf. A000566, A097563, A274046, A279280, A350196, A350197, A350199.

A350199 a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero octagonal numbers in exactly n ways, or 0 if no such integer exists.

Original entry on oeis.org

1, 105, 238, 302, 342, 406, 570, 622, 639, 686, 758, 750, 822, 815, 862, 883, 926, 983, 1027, 966, 995, 987, 1099, 1091, 1159, 1142, 1143, 1183, 1227, 1171, 1231, 1163, 1315, 1295, 1296, 1275, 1372, 1267, 1371, 1343, 1375, 1399, 1476, 1411, 1403, 1407, 1463, 1451, 1508, 1507

Offset: 1

Ilya Gutkovskiy, Dec 19 2021

nonn

Eric Weisstein's World of Mathematics, Octagonal Number

Cf. A000567, A097563, A274046, A279281, A350196, A350197, A350198.

A350207 a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero n-gonal numbers in exactly n ways, or 0 if no such integer exists.

Original entry on oeis.org

25, 65, 144, 305, 456, 622, 731, 1006, 1434, 1499, 1711, 1806, 2446, 2742, 3001, 3051, 3544, 3699, 3962, 4345, 5362, 5039, 5756, 5712, 6251, 6655, 7399, 7698, 7591, 8304, 8673, 9241, 9362, 9299, 10312, 10606, 11121, 10736, 12113, 12737, 12934

Offset: 3

Ilya Gutkovskiy, Dec 19 2021

nonn

Eric Weisstein's World of Mathematics, Polygonal Number

Cf. A057145, A097563, A274046, A350196, A350197, A350198, A350199, A350209, A350210.

A350203 a(n) is the smallest positive integer which can be represented as the sum of distinct centered triangular numbers in exactly n ways, or 0 if no such integer exists.

Original entry on oeis.org

1, 46, 65, 110, 150, 160, 196, 246, 254, 255, 245, 281, 355, 309, 331, 339, 335, 349, 399, 412, 380, 439, 385, 425, 435, 395, 466, 440, 444, 476, 494, 470, 471, 485, 480, 475, 535, 521, 516, 520, 588, 525, 571, 585, 589, 560, 602, 565, 594, 561

Offset: 1

Ilya Gutkovskiy, Dec 19 2021

nonn

Eric Weisstein's World of Mathematics, Centered Triangular Number

Cf. A005448, A274046, A281081, A350195, A350204.

cp's OEIS Frontend

A275154 Smallest positive integer which can be represented as the sum of distinct positive cubes in exactly n ways, or 0 if no such integer exists.

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A350205 a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero tetrahedral numbers in exactly n ways, or 0 if no such integer exists.

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A350196 a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero pentagonal numbers in exactly n ways, or 0 if no such integer exists.

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A350197 a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero hexagonal numbers in exactly n ways, or 0 if no such integer exists.

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A350198 a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero heptagonal numbers in exactly n ways, or 0 if no such integer exists.

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A350199 a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero octagonal numbers in exactly n ways, or 0 if no such integer exists.

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A350207 a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero n-gonal numbers in exactly n ways, or 0 if no such integer exists.

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A350203 a(n) is the smallest positive integer which can be represented as the sum of distinct centered triangular numbers in exactly n ways, or 0 if no such integer exists.

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