A308738 Numbers that can be written as the sum of five distinct nonnegative cubes.

100, 161, 198, 217, 224, 225, 252, 289, 308, 315, 316, 350, 369, 376, 377, 379, 406, 413, 414, 416, 432, 433, 435, 440, 442, 443, 477, 496, 503, 504, 533, 540, 541, 548, 559, 560, 567, 568, 585, 587, 594, 595, 604, 611, 612, 624, 631, 632, 646, 650, 651, 658, 665, 672, 673, 685, 692, 693, 702

Offset

1,1

Comments

It is possible that this sequence contains all sufficiently large numbers.

The smallest number with more than one representation is 756 = 0^3 + 1^3 + 3^3 + 6^3 + 8^3 = 2^3 + 4^3 + 5^3 + 6^3 + 7^3.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3)=198 is in the sequence because 198 = 0^3 + 1^3 + 2^3 + 4^3 + 5^3.

Maple

N:= 1000: # to get all terms <= N
S:= {}:
for a from 0 while 5*a^3 < N do
  for b from a+1 while a^3 + 4*b^3 < N do
    for c from b+1 while a^3 + b^3 + 3*c^3 < N do
      for d from c+1 while a^3 + b^3 + c^3 + 2*d^3 < N do
        S:= S union {seq(a^3 + b^3 + c^3 + d^3 + e^3, e=d+1..floor((N-a^3-b^3-c^3-d^3)^(1/3)))}
od od od od:
sort(convert(S, list));

Mathematica

With[{nn=10}, Select[Union[Total/@Subsets[Range[0, nn]^3, {5}]], #<=nn^3-36&]] (* Harvey P. Dale, Nov 19 2022 *)

Crossrefs

Sequence in context: A004262 A004263 A004264 * A025411 A025408 A068805

Adjacent sequences: A308735 A308736 A308737 * A308739 A308740 A308741

Keyword

nonn

Author

Robert Israel, Jun 21 2019

Status

approved