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A308738
Numbers that can be written as the sum of five distinct nonnegative cubes.
1
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
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
KEYWORD
nonn
AUTHOR
Robert Israel, Jun 21 2019
STATUS
approved