A048926 Numbers that are the sum of 5 positive cubes in exactly 1 way.

5, 12, 19, 26, 31, 33, 38, 40, 45, 52, 57, 59, 64, 68, 71, 75, 78, 82, 83, 89, 90, 94, 96, 97, 101, 108, 109, 115, 116, 120, 127, 129, 131, 134, 135, 136, 138, 143, 145, 146, 150, 152, 153, 155, 162, 164, 169, 171, 172, 176, 181, 183, 188, 190, 192, 194, 195

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• fini

Comments

It appears that this sequence has 11062 terms, the last of which is 1685758. This means that all numbers greater than 1685758 can be written as the sum of five 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..11062
• Eric Weisstein's World of Mathematics, Cubic Number.

Crossrefs

Cf. A003328, A048927.

Cf. A057906 (numbers not the sum of five positive cubes)

Programs

Mathematica

Select[ Range[200], Count[ PowersRepresentations[#, 5, 3], r_ /; FreeQ[r, 0]] == 1 &] (* Jean-François Alcover, Oct 23 2012 *)

Python

from collections import Counter
from itertools import combinations_with_replacement as combs_with_rep
def aupto(lim):
  s = filter(lambda x: x<=lim, (i**3 for i in range(1, int(lim**(1/3))+2)))
  s2 = filter(lambda x: x<=lim, (sum(c) for c in combs_with_rep(s, 5)))
  s2counts = Counter(s2)
  return sorted(k for k in s2counts if s2counts[k] == 1)
print(aupto(196)) # Michael S. Branicky, May 12 2021