A345542 Numbers that are the sum of nine positive cubes in three or more ways.

224, 231, 238, 245, 250, 257, 259, 264, 271, 276, 278, 280, 283, 285, 287, 290, 292, 294, 297, 299, 301, 302, 309, 311, 313, 315, 316, 318, 320, 322, 327, 334, 335, 337, 339, 341, 346, 348, 350, 353, 355, 357, 362, 365, 372, 374, 376, 379, 381, 383, 386, 387

Offset

1,1

Links

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Example

231 is a term because 231 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 5^3 = 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3.

Mathematica

Select[Range[400], Length[Select[PowersRepresentations[#, 9, 3], FreeQ[ #, 0]&]]> 2&] (* Harvey P. Dale, Jan 04 2022 *)

Prog

(Python)
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1, 1000)]
for pos in cwr(power_terms, 9):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 3])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A345500, A345533, A345541, A345543, A345551, A345587, A345795.

Sequence in context: A162604 A296896 A050241 * A345543 A345796 A046296

Adjacent sequences: A345539 A345540 A345541 * A345543 A345544 A345545

Keyword

nonn

Author

David Consiglio, Jr., Jun 20 2021

Extensions

Definition corrected by Harvey P. Dale, Jan 04 2022

Status

approved