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A374417 a(n) is the smallest number which can be represented as the sum of n distinct positive cubes in exactly 2 ways, or -1 if no such number exists.

%I A374417 #19 Jul 12 2024 11:28:05
%S A374417 -1,1729,1009,1036,1161,1504,1899,2512,3024,4355,6552,9296,11648,
%T A374417 14392,19305,25137,30997,35757,44092,53353,64001,76168,88669,104625,
%U A374417 122201,144153,167401,191772,216161,245952,278757,312993,352297,393822,434295,489167,541081,605656,671446
%N A374417 a(n) is the smallest number which can be represented as the sum of n distinct positive cubes in exactly 2 ways, or -1 if no such number exists.
%H A374417 David A. Corneth, <a href="/A374417/b374417.txt">Table of n, a(n) for n = 1..675</a>
%H A374417 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%e A374417 a(2) = 1729 = 1^3 + 12^3 = 9^3 + 10^3.
%e A374417 a(3) = 1009 = 1^3 + 2^3 + 10^3 = 4^3 + 6^3 + 9^3.
%p A374417 G:= mul(1+t*x^(i^3), i=1..35):
%p A374417 R:= -1:
%p A374417 for m from 2 do
%p A374417   C:= expand(coeff(G,t,m)):
%p A374417   C2:= convert(select(s -> subs(x=1,s)=2, C),list);
%p A374417   v:= min(map(degree,C2));
%p A374417   if v >= 36^3 + add(i^3,i=1..m-1) then break fi;
%p A374417   R:= R,v;
%p A374417 od:
%p A374417 R; # _Robert Israel_, Jul 08 2024
%Y A374417 Cf. A000537, A011541, A350270, A374287.
%K A374417 sign
%O A374417 1,2
%A A374417 _Ilya Gutkovskiy_, Jul 08 2024
%E A374417 a(15)-a(27) from _Robert Israel_, Jul 08 2024
%E A374417 a(28)-a(39) from _Michael S. Branicky_, Jul 10 2024