A345804 Numbers that are the sum of ten cubes in exactly two ways.

73, 80, 99, 134, 136, 141, 148, 155, 160, 162, 167, 169, 174, 176, 183, 186, 188, 190, 192, 193, 195, 199, 202, 204, 206, 209, 211, 212, 213, 214, 216, 218, 221, 223, 228, 230, 235, 240, 244, 247, 249, 254, 262, 266, 269, 270, 273, 274, 290, 292, 297, 304

Offset: 1

Author

David Consiglio, Jr., Jun 26 2021

Keywords

• nonn

Comments

Differs from A345550 at term 22 because 197 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 4^3 + 5^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3 + 4^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 5^3.

Likely finite.

Examples

			80 is a term because 80 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 3^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..90

Crossrefs

Cf. A345550, A345794, A345803, A345805, A345854.

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, 10):
    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])