A345784 Numbers that are the sum of eight cubes in exactly two ways.

132, 139, 158, 160, 167, 174, 181, 186, 193, 195, 197, 200, 212, 216, 219, 238, 244, 251, 258, 265, 272, 277, 288, 296, 298, 300, 301, 303, 307, 314, 315, 317, 321, 322, 327, 328, 329, 333, 334, 336, 338, 340, 341, 348, 350, 352, 356, 359, 360, 361, 363, 366

Offset

1,1

Comments

Differs from A345532 at term 16 because 223 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 6^3 = 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 4^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3 + 5^3.

Likely finite.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..173

Example

139 is a term because 139 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 4^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 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, 8):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 2])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A345532, A345774, A345783, A345785, A345794, A345834.

Sequence in context: A211407 A108601 A345532 * A039603 A354812 A030026

Adjacent sequences: A345781 A345782 A345783 * A345785 A345786 A345787

Keyword

nonn

Author

David Consiglio, Jr., Jun 26 2021

Status

approved