This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A275154 #101 Aug 04 2025 15:54:20 %S A275154 1,216,729,1072,1736,1737,2465,2800,2808,3619,3276,4257,4131,4662, %T A275154 4473,5292,5265,5328,6084,5481,6202,5985,6777,6840,7056,7372,7659, %U A275154 7560,7588,7380,7596,7722,8037,8190,8576,8064,8316,9297,9549,8380,9045,9261,9451,9360,8919,10044,9108 %N 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. %C A275154 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 %H A275154 David A. Corneth, <a href="/A275154/b275154.txt">Table of n, a(n) for n = 1..10000</a> %H A275154 Zhao Hui Du, <a href="/A275154/a275154_1.pdf">Proof for the theorem related to Q(k,u)</a> %H A275154 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a> %F A275154 A279329(a(n)) = n. %e A275154 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. %Y A275154 Cf. A003997, A097563, A274046, A279329. %K A275154 nonn %O A275154 1,2 %A A275154 _Ilya Gutkovskiy_, Jun 01 2017