A345774 Numbers that are the sum of seven cubes in exactly two ways.

131, 159, 166, 173, 185, 192, 211, 236, 243, 257, 264, 269, 274, 276, 288, 290, 292, 295, 299, 300, 302, 307, 309, 311, 314, 320, 321, 325, 332, 333, 337, 339, 340, 344, 348, 351, 353, 355, 358, 359, 360, 363, 372, 384, 385, 386, 388, 389, 393, 395, 398, 403

Offset: 1

Author

David Consiglio, Jr., Jun 26 2021

Keywords

• nonn

Comments

Differs from A345520 at term 8 because 222 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 6^3 = 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 4^3 = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3 + 5^3.

Likely finite.

Examples

			159 is a term because 159 = 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..355

Crossrefs

Cf. A048930, A345520, A345773, A345775, A345784, A345824.

Programs

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, 7):
    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])