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

1,1

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A003329, A048930, A048931.

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

Sequence in context: A109235 A189523 A003329 * A187393 A356059 A337141

Adjacent sequences: A048926 A048927 A048928 * A048930 A048931 A048932

Keyword

nonn,fini

Author

Eric W. Weisstein

Status

approved