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

Author

Ilya Gutkovskiy, Jun 01 2017

Keywords

• nonn

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

Examples

			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.
		

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

Crossrefs

Cf. A003997, A097563, A274046, A279329.

Formula

A279329(a(n)) = n.