A350209 -id:A350209 - cp's OEIS frontend

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.

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

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.

A352975 a(n) is the smallest number which can be represented as the sum of n distinct centered n-gonal numbers in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

96, 192, 330, 504, 840, 1304, 1872, 2910, 3971, 5340, 6851, 8932, 11700, 14496, 18258, 22410, 27265, 32620, 39606, 47124, 55545, 65448, 76050, 87854, 101925, 116956, 134125, 152340, 173538, 195424, 220473, 246942, 276570, 306756, 340918, 377644, 418821, 462720

Offset: 3

Ilya Gutkovskiy, Apr 13 2022

nonn

If a(n) exists, then n divides a(n). - Thomas Scheuerle, Apr 13 2022

			For n = 3: 96 = 1 + 10 + 85 = 1 + 31 + 64 = 19 + 31 + 46.

Eric Weisstein's World of Mathematics, Centered Polygonal Number

Cf. A101321, A350209, A350397, A350405.

a(n) >= n*binomial(n + 2, 3) + n, if a(n) exists. - Thomas Scheuerle, Apr 13 2022

a(10)-a(16) from Thomas Scheuerle, Apr 13 2022

a(17)-a(40) from Michael S. Branicky, May 19 2022

cp's OEIS Frontend

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.

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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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A352975 a(n) is the smallest number which can be represented as the sum of n distinct centered n-gonal numbers in exactly n ways, or -1 if no such number exists.

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