A350207 -id:A350207 - cp's OEIS frontend

A350405 a(n) is the smallest number which can be represented as the sum of n distinct nonzero n-gonal numbers in exactly n ways, or 0 if no such number exists.

37, 142, 285, 536, 911, 1268, 1909, 2713, 3876, 5179, 6891, 8901, 11190, 14384, 18087, 21697, 27055, 32166, 39111, 46560, 53892, 64412, 73949, 86778, 98202, 113635, 130088, 148051, 167505, 190968, 214955, 240143, 269775, 297615, 331201, 367429, 409179, 451340, 497830

Offset: 3

Ilya Gutkovskiy, Dec 29 2021

nonn

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

David A. Corneth, Table of n, a(n) for n = 3..102
Eric Weisstein's World of Mathematics, Polygonal Number

Cf. A006484, A025443, A057145, A307598, A350207, A350241, A350288.

Do[i=1;While[b=PolygonalNumber[n,Range@i++];!IntegerQ[t=Min[First/@Select[Tally[Select[Total/@Subsets[b,{n}],#<=Max@b&]],Last@#==n&]]]];Print@t,{n,3,10}] (* Giorgos Kalogeropoulos, Dec 30 2021 *)

a(n) >= A006484(n). - David A. Corneth, Dec 30 2021

a(10)-a(31) from Michael S. Branicky, Dec 29 2021

More terms from David A. Corneth, Dec 30 2021

A350210 a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero n-gonal pyramidal numbers in exactly n ways, or 0 if no such integer exists.

Original entry on oeis.org

140, 490, 1055, 1872, 2610, 4255, 5011, 8708, 7497, 10819, 12860, 15636, 18055, 24275, 27373, 28146, 30826, 38178, 41849, 44025, 36165, 47621, 57896, 64648, 60064, 67125, 71975, 81820, 77701, 91584, 91320, 99835, 98916, 108686, 112606, 123180, 120919, 142270

Offset: 3

Ilya Gutkovskiy, Dec 19 2021

nonn

			For n = 3: 140 = 1 + 20 + 35 + 84 = 56 + 84 = 20 + 120. - _Martin Ehrenstein_, Jan 09 2022

Martin Ehrenstein, Table of n, a(n) for n = 3..1002
Eric Weisstein's World of Mathematics, Pyramidal Number

Cf. A080851, A350205, A350206, A350207, A350209, A350397.

a(35)-a(40) from Martin Ehrenstein, Jan 09 2022

A350209 a(n) is the smallest positive integer which can be represented as the sum of distinct centered n-gonal numbers in exactly n ways, or 0 if no such integer exists.

Original entry on oeis.org

65, 151, 330, 316, 515, 645, 888, 824, 1017, 1348, 1474, 1614, 1655, 2006, 2233, 2255, 2779, 2805, 2882, 2865, 3364, 3653, 3930, 4035, 4325, 4765, 4675, 5016, 4904, 5446, 5913, 5990, 6061, 6954, 6850, 7681, 8313, 7846, 7591, 9035, 8736

Offset: 3

Ilya Gutkovskiy, Dec 19 2021

nonn

Eric Weisstein's World of Mathematics, Centered Polygonal Number

Cf. A101321, A350195, A350203, A350204, A350207, A350210.

A363253 a(n) is the smallest n-gonal number which can be represented as the sum of distinct nonzero n-gonal numbers in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

28, 121, 210

Offset: 3

Ilya Gutkovskiy, May 23 2023

a(8) = 736, a(9) = 969.

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

Eric Weisstein's World of Mathematics, Polygonal Number

Cf. A057145, A350207, A350405, A350423.

cp's OEIS Frontend

A350405 a(n) is the smallest number which can be represented as the sum of n distinct nonzero n-gonal numbers in exactly n ways, or 0 if no such number exists.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A350210 a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero n-gonal pyramidal numbers in exactly n ways, or 0 if no such integer exists.

Views

Author

Keywords

Examples

Links

Crossrefs

Extensions

A350209 a(n) is the smallest positive integer which can be represented as the sum of distinct centered n-gonal numbers in exactly n ways, or 0 if no such integer exists.

Views

Author

Keywords

Links

Crossrefs

A363253 a(n) is the smallest n-gonal number which can be represented as the sum of distinct nonzero n-gonal numbers in exactly n ways, or -1 if no such number exists.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs