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

1,2

Comments

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

Links

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

Formula

A279329(a(n)) = n.

Example

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.

Crossrefs

Cf. A003997, A097563, A274046, A279329.

Sequence in context: A074266 A208089 A333316 * A066890 A242296 A223507

Adjacent sequences: A275151 A275152 A275153 * A275155 A275156 A275157

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 01 2017

Status

approved