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

1,1

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A003328, A048927.

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

Sequence in context: A063614 A048928 A003328 * A047704 A043413 A017041

Adjacent sequences: A048923 A048924 A048925 * A048927 A048928 A048929

Keyword

nonn,fini

Author

Eric W. Weisstein

Status

approved