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A345542
Numbers that are the sum of nine positive cubes in three or more ways.
8
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
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])
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition corrected by Harvey P. Dale, Jan 04 2022
STATUS
approved