A350206 -id:A350206 - cp's OEIS frontend

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.

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.

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

A360218 a(n) is the smallest positive integer which can be represented as the sum of n distinct nonzero square pyramidal numbers in exactly n ways, or -1 if no such integer exists.

Original entry on oeis.org

1, 5580, 2814, 1980, 1595, 1700, 2175, 2415, 2830, 3740, 4810, 5995, 7610, 9240, 11380, 13896, 16506, 19735, 23150, 27441, 32085, 36721, 42755, 49570, 56610, 65135, 73165, 83021, 93835, 105671, 118255, 132545, 147546, 163516, 182155, 201040, 222371, 244280, 267856

Offset: 1

Ilya Gutkovskiy, Jan 30 2023

nonn

			For n = 3: 2814 = 14 + 1015 + 1785 = 55 + 650 + 2109 = 140 + 204 + 2470.

Michael S. Branicky, Table of n, a(n) for n = 1..80
Eric Weisstein's World of Mathematics, Square Pyramidal Number

Cf. A000330, A350206, A350241, A350397, A360217.

a(18)-a(33) from Michael S. Branicky, Feb 04 2023

a(34) and beyond from Michael S. Branicky, Feb 18 2023

cp's OEIS Frontend

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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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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A360218 a(n) is the smallest positive integer which can be represented as the sum of n distinct nonzero square pyramidal numbers in exactly n ways, or -1 if no such integer exists.

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