A342326 -id:A342326 - cp's OEIS frontend

A374141 a(n) is the smallest number which can be represented as the sum of two distinct nonzero hexagonal numbers in exactly n ways, or -1 if no such number exists.

7, 384, 4995, 51106, 204805, 483031, 2443431, 4674256, 10476781, 17272531, 25600656, 60765331, 90406956, 206602126, 332808531, 481676406, 303826656, 435211156, 789949306, 1406495106, 2260173906, 2704798281, 3220562556, 4435869181, 5165053156, 5309576106, 9818788281

Offset: 1

Ilya Gutkovskiy, Jun 28 2024

nonn

			a(2) = 384 = 6 + 378 = 153 + 231.

Michael S. Branicky, Table of n, a(n) for n = 1..39
Michael S. Branicky, Python program for A374141, A374142, and A374143
Eric Weisstein's World of Mathematics, Hexagonal Number

Cf. A000384, A093195, A332989, A342326, A374142, A374143.

Python
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# see linked program
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a(9)-a(27) from Michael S. Branicky, Jun 29 2024

A374142 a(n) is the smallest number which can be represented as the sum of two distinct nonzero heptagonal numbers in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

8, 617, 8726, 255575, 1339801, 2419165, 9402323, 25764500, 35486953, 144568133, 385495261, 735503569, 638279039, 1183071664, 1571634527, 4449717748, 3584182298, 3871587494, 5693954599, 27084640649, 24205505111, 32489035067, 31973745058, 38935021406, 47570693867, 44749048300, 53075499329

Offset: 1

Ilya Gutkovskiy, Jun 28 2024

nonn

			a(2) = 617 = 1 + 616 = 148 + 469.

Michael S. Branicky, Python program for A374141, A374142, and A374143
Eric Weisstein's World of Mathematics, Heptagonal Number

Cf. A000566, A093195, A332989, A342326, A374141, A374143.

Python
```
# see linked program
```

a(8)-a(27) from Michael S. Branicky, Jun 29 2024

A374143 a(n) is the smallest number which can be represented as the sum of two distinct nonzero octagonal numbers in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

9, 1053, 12641, 68141, 365641, 953181, 2830641, 6232341, 13969041, 23211261, 104733741, 84994021, 175873641, 159851141, 538547641, 602713041, 810204416, 1019740041, 1053265741, 1972957241, 3339356041, 5914492241, 6886737541, 6388758241, 8902368041, 7858982841, 4942246941, 18439299341, 26639916441

Offset: 1

Ilya Gutkovskiy, Jun 28 2024

nonn

			a(2) = 1053 = 8 + 1045 = 408 + 645.

Michael S. Branicky, Table of n, a(n) for n = 1..38
Michael S. Branicky, Python program for A374141, A374142, and A374143
Eric Weisstein's World of Mathematics, Octagonal Number

Cf. A000567, A093195, A332989, A342326, A374141, A374142.

Python
```
# see linked program
```

a(9)-a(29) from Michael S. Branicky, Jun 29 2024

A374144 a(n) is the smallest number which can be represented as the sum of two distinct nonzero n-gonal numbers in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

81, 1105, 205427, 483031, 9402323, 6232341, 79324200, 768459127, 2265692766, 2413112833, 6737406626, 150437989675, 45319359337, 15140186701

Offset: 3

Ilya Gutkovskiy, Jun 28 2024

			a(3) = 81 = 3 + 78 = 15 + 66 = 36 + 45.

Eric Weisstein's World of Mathematics, Polygonal Number
Michael S. Branicky, Python program for A374144

Cf. A057145, A093195, A332989, A342326, A350405, A374141, A374142, A374143.

Python
```
# see linked program
```

a(9)-a(16) from Michael S. Branicky, Jun 30 2024

A350288 a(n) is the smallest number which can be represented as the sum of n distinct nonzero triangular numbers in exactly n ways, or 0 if no such number exists.

Original entry on oeis.org

1, 16, 37, 64, 83, 128, 177, 204, 270, 352, 430, 533, 632, 764, 893, 1102, 1256, 1443, 1630, 1855, 2141, 2384, 2699, 3053, 3378, 3753, 4176, 4620, 5068, 5570, 6107, 6654, 7253, 7904, 8526, 9241, 9975, 10699, 11533, 12401, 13301, 14189, 15179, 16233, 17286, 18412

Offset: 1

Ilya Gutkovskiy, Dec 23 2021

nonn

			For n = 2: 16 = 1 + 15 = 6 + 10.
For n = 3: 37 = 1 + 15 + 21 = 3 + 6 + 28 = 6 + 10 + 21.

Cf. A000217, A265134, A307597, A307598, A341021-A341027, A342326, A350241.

More terms from Jinyuan Wang, Dec 26 2021

A374806 a(n) is the smallest number which can be represented as the sum of 3 distinct nonzero triangular numbers in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

10, 19, 37, 52, 82, 109, 136, 241, 226, 217, 247, 364, 427, 457, 541, 532, 577, 637, 961, 721, 787, 1066, 1102, 1381, 1267, 1564, 1192, 1396, 1816, 1501, 1612, 1927, 1942, 2242, 1792, 2842, 2587, 2557, 2422, 2866, 2887, 3181, 3271, 3412, 4126

Offset: 1

Ilya Gutkovskiy, Jul 20 2024

nonn

			a(3) = 37 = 1 + 15 + 21 = 3 + 6 + 28 = 6 + 10 + 21.

Eric Weisstein's World of Mathematics, Triangular Number

Cf. A000217, A025415, A342326, A374807.

A374807 a(n) is the smallest number which can be represented as the sum of 4 distinct nonzero triangular numbers in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

20, 38, 47, 64, 73, 92, 97, 110, 127, 115, 130, 164, 185, 172, 208, 157, 199, 235, 247, 232, 220, 272, 277, 304, 280, 361, 262, 307, 319, 391, 322, 292, 495, 415, 337, 367, 370, 382, 478, 482, 412, 409, 445, 430, 467, 500, 427, 532, 493

Offset: 1

Ilya Gutkovskiy, Jul 20 2024

nonn

			a(3) = 47 = 1 + 3 + 15 + 28 = 1 + 10 + 15 + 21 = 3 + 6 + 10 + 28.

Eric Weisstein's World of Mathematics, Triangular Number

Cf. A000217, A025417, A342326, A374806.

cp's OEIS Frontend

A374141 a(n) is the smallest number which can be represented as the sum of two distinct nonzero hexagonal numbers in exactly n ways, or -1 if no such number exists.

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A374142 a(n) is the smallest number which can be represented as the sum of two distinct nonzero heptagonal numbers in exactly n ways, or -1 if no such number exists.

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A374143 a(n) is the smallest number which can be represented as the sum of two distinct nonzero octagonal numbers in exactly n ways, or -1 if no such number exists.

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A374144 a(n) is the smallest number which can be represented as the sum of two distinct nonzero n-gonal numbers in exactly n ways, or -1 if no such number exists.

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A350288 a(n) is the smallest number which can be represented as the sum of n distinct nonzero triangular numbers in exactly n ways, or 0 if no such number exists.

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A374806 a(n) is the smallest number which can be represented as the sum of 3 distinct nonzero triangular numbers in exactly n ways, or -1 if no such number exists.

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Author

Keywords

Examples

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A374807 a(n) is the smallest number which can be represented as the sum of 4 distinct nonzero triangular numbers in exactly n ways, or -1 if no such number exists.

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Author

Keywords

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