A345795 Numbers that are the sum of nine cubes in exactly three ways.

231, 238, 245, 250, 259, 271, 276, 278, 280, 285, 287, 290, 292, 294, 297, 299, 301, 302, 309, 311, 313, 315, 316, 318, 322, 327, 334, 335, 337, 339, 341, 346, 350, 353, 357, 362, 365, 379, 386, 387, 388, 391, 393, 394, 395, 397, 398, 405, 412, 418, 420, 421

Offset

1,1

Comments

Differs from A345542 at term 1 because 224 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 6^3 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 4^3 = 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3 + 5^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3.

Likely finite.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..136

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.

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. A345542, A345785, A345794, A345796, A345805, A345845.

Sequence in context: A156742 A031965 A316095 * A088289 A046009 A350367

Adjacent sequences: A345792 A345793 A345794 * A345796 A345797 A345798

Keyword

nonn

Author

David Consiglio, Jr., Jun 26 2021

Status

approved