A345805 Numbers that are the sum of ten cubes in exactly three ways.

197, 239, 246, 253, 260, 267, 277, 279, 281, 293, 295, 298, 300, 302, 303, 305, 309, 312, 316, 317, 319, 324, 326, 329, 330, 335, 336, 338, 340, 343, 344, 345, 351, 352, 354, 358, 361, 362, 364, 365, 368, 370, 379, 386, 387, 388, 392, 394, 395, 396, 402, 406

Offset

1,1

Comments

Differs from A345551 at term 2 because 225 = 1^3 + 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 + 1^3 + 3^3 + 4^3 + 4^3 + 4^3 = 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3 + 5^3 = 1^3 + 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..93

Example

225 is a term because 225 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 5^3 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 3^3 = 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3 = 1^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3.

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, 10):
    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. A345551, A345795, A345804, A345806, A345855.

Sequence in context: A345551 A051371 A127339 * A142121 A142274 A142624

Adjacent sequences: A345802 A345803 A345804 * A345806 A345807 A345808

Keyword

nonn

Author

David Consiglio, Jr., Jun 26 2021

Status

approved