A003998 Numbers that are a sum of distinct positive cubes in more than one way.

216, 217, 224, 225, 540, 559, 560, 567, 568, 728, 729, 736, 737, 756, 757, 764, 793, 801, 820, 828, 854, 855, 862, 863, 881, 882, 889, 890, 918, 919, 926, 927, 945, 946, 953, 954, 980, 981, 1008, 1009, 1036, 1044, 1045, 1071, 1072, 1073, 1079, 1080

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Links

• Zak Seidov and Robert Israel, Table of n, a(n) for n = 1..10000 (n = 1..1038 from Zak Seidov)

Crossrefs

Cf. A001239.

Programs

Maple

F:= proc(x,y) option remember;
  if y = 0 then 1
  elif y < x^3 then 0
  elif y = x^3 then 1
  else procname(x+1,y) + procname(x+1,y-x^3)
  fi
end proc:
select(t -> F(1,t) > 1, [$1..10000]); # Robert Israel, Dec 31 2015

Mathematica

ok[n_] := Length[ Select[ Union[ Union /@ Flatten[ Table[ DeleteCases[ PowersRepresentations[n, k, 3], 0, 2], {k, 1, Floor[(n-1)^(1/3)]}], 1]], Total[#^3] == n & , 2]] == 2; Reap[ Do[ If[ ok[n], Print[n]; Sow[n]], {n, 1, 1100}]][[2, 1]](* Jean-François Alcover, Feb 23 2012 *)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Mar 20 2000