A048929 Numbers that are the sum of 6 positive cubes in exactly 1 way.

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, 160, 161, 162, 163, 170

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• fini

Comments

It appears that this sequence has 841 terms, the last of which is 19417. This means that all numbers greater than 19417 can be written as the sum of six positive cubes in at least two ways. - T. D. Noe, Dec 13 2006

Links

• T. D. Noe, Table of n, a(n) for n=1..841
• Eric Weisstein's World of Mathematics, Cubic Number.

Crossrefs

Cf. A003329, A048930, A048931.

Cf. A057907 (numbers not the sum of six positive cubes)

Programs

Mathematica

Select[ Range[200], Length[ Select[ PowersRepresentations[#, 6, 3], And @@ (Positive /@ #) &]] == 1 &] (* Jean-François Alcover, Oct 25 2012 *)

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 if counts[k]==1)
print(aupto(20000)) # Michael S. Branicky, Jun 13 2021