A003329 - OEIS

A003329

Numbers that are the sum of 6 positive cubes.

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

David A. Corneth, Table of n, a(n) for n = 1..10000

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