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A003329 Numbers that are the sum of 6 positive cubes. 45
6, 13, 20, 27, 32, 34, 39, 41, 46, 48, 53, 58, 60, 65, 67, 69, 72, 76, 79, 83, 84, 86, 90, 91, 95, 97, 98, 102, 104, 105, 109, 110, 116, 117, 121, 123, 124, 128, 130, 132, 135, 136, 137, 139, 142, 143, 144, 146, 147, 151, 153, 154, 156, 158, 160, 161, 162, 163, 165, 170 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
As the order of addition doesn't matter we can assume terms are in increasing order. - David A. Corneth, Aug 01 2020
LINKS
Eric Weisstein's World of Mathematics, Cubic Number.
EXAMPLE
From David A. Corneth, Aug 01 2020: (Start)
1647 is in the sequence as 1647 = 3^3 + 3^3 + 5^3 + 5^3 + 7^3 + 10^3.
3319 is in the sequence as 3319 = 5^3 + 5^3 + 5^3 + 6^3 + 10^3 + 12^3.
4038 is in the sequence as 4038 = 3^3 + 3^3 + 6^3 + 8^3 + 8^3 + 14^3. (End)
MATHEMATICA
max = 200; cmax = Ceiling[(max - 5)^(1/3)]; cc = Array[c, 6]; iter = Sequence @@ Transpose[ {cc, Join[{1}, Most[cc]], Table[cmax, {6}]}]; Union[ Reap[ Do[ a = Total[cc^3]; If[a <= max, Sow[a]], Evaluate[iter]]][[2, 1]]] (* Jean-François Alcover, Oct 23 2012 *)
PROG
(PARI) (A003329_upto(N, k=6, m=3)=[i|i<-[1..#N=sum(n=1, sqrtnint(N, m), 'x^n^m, O('x^N))^k], polcoef(N, i)])(200) \\ M. F. Hasler, Aug 02 2020
(Python)
from collections import Counter
from itertools import combinations_with_replacement as multi_combs
def aupto(lim):
c = filter(lambda x: x<=lim, (i**3 for i in range(1, int(lim**(1/3))+2)))
s = filter(lambda x: x<=lim, (sum(mc) for mc in multi_combs(c, 6)))
counts = Counter(s)
return sorted(k for k in counts)
print(aupto(170)) # Michael S. Branicky, Jun 13 2021
CROSSREFS
Cf. A057907 (Complement)
Cf. A###### (x, y) = Numbers that are the sum of x nonzero y-th powers:
A000404 (2, 2), A000408 (3, 2), A000414 (4, 2), A047700 (5, 2),
A003325 (2, 3), A003072 (3, 3), A003327 .. A003335 (4 .. 12, 3),
A003336 .. A003346 (2 .. 12, 4), A003347 .. A003357 (2 .. 12, 5),
A003358 .. A003368 (2 .. 12, 6), A003369 .. A003379 (2 .. 12, 7),
A003380 .. A003390 (2 .. 12, 8), A003391 .. A004801 (2 .. 12, 9),
A004802 .. A004812 (2 .. 12, 10), A004813 .. A004823 (2 .. 12, 11).
Sequence in context: A309434 A109235 A189523 * A048929 A187393 A356059
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Eric W. Weisstein
STATUS
approved

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Last modified April 23 19:56 EDT 2024. Contains 371916 sequences. (Running on oeis4.)