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.

-1, 1729, 1009, 1036, 1161, 1504, 1899, 2512, 3024, 4355, 6552, 9296, 11648, 14392, 19305, 25137, 30997, 35757, 44092, 53353, 64001, 76168, 88669, 104625, 122201, 144153, 167401, 191772, 216161, 245952, 278757, 312993, 352297, 393822, 434295, 489167, 541081, 605656, 671446

Offset: 1

Author

Ilya Gutkovskiy, Jul 08 2024

Keywords

• sign

Examples

			a(2) = 1729 = 1^3 + 12^3 = 9^3 + 10^3.
a(3) = 1009 = 1^3 + 2^3 + 10^3 = 4^3 + 6^3 + 9^3.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..675
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A000537, A011541, A350270, A374287.

Programs

Maple

G:= mul(1+t*x^(i^3), i=1..35):
R:= -1:
for m from 2 do
  C:= expand(coeff(G,t,m)):
  C2:= convert(select(s -> subs(x=1,s)=2, C),list);
  v:= min(map(degree,C2));
  if v >= 36^3 + add(i^3,i=1..m-1) then break fi;
  R:= R,v;
od:
R; # Robert Israel, Jul 08 2024

Extensions

a(15)-a(27) from Robert Israel, Jul 08 2024

a(28)-a(39) from Michael S. Branicky, Jul 10 2024