A345780 Numbers that are the sum of seven cubes in exactly eight ways.

1385, 1515, 1552, 1557, 1585, 1587, 1603, 1613, 1622, 1655, 1665, 1674, 1681, 1718, 1719, 1739, 1741, 1746, 1753, 1755, 1765, 1767, 1782, 1793, 1805, 1809, 1811, 1818, 1819, 1826, 1828, 1830, 1833, 1838, 1856, 1870, 1873, 1881, 1901, 1905, 1931, 1935, 1937

Offset: 1

Author

David Consiglio, Jr., Jun 26 2021

Keywords

• nonn

Comments

Differs from A345526 at term 2 because 1496 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 9^3 + 9^3 = 1^3 + 1^3 + 2^3 + 3^3 + 4^3 + 4^3 + 11^3 = 1^3 + 1^3 + 4^3 + 4^3 + 5^3 + 8^3 + 9^3 = 1^3 + 2^3 + 2^3 + 4^3 + 7^3 + 7^3 + 9^3 = 1^3 + 5^3 + 5^3 + 6^3 + 7^3 + 7^3 + 7^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 5^3 + 11^3 = 2^3 + 3^3 + 3^3 + 3^3 + 4^3 + 7^3 + 10^3 = 2^3 + 3^3 + 6^3 + 6^3 + 7^3 + 7^3 + 7^3 = 4^3 + 4^3 + 4^3 + 4^3 + 6^3 + 8^3 + 8^3.

Likely finite.

Examples

			1496 is a term because 1496 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 8^3 + 8^3 = 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 3^3 + 10^3 = 1^3 + 1^3 + 3^3 + 3^3 + 4^3 + 7^3 + 8^3 = 1^3 + 2^3 + 2^3 + 3^3 + 6^3 + 6^3 + 8^3 = 1^3 + 4^3 + 4^3 + 5^3 + 6^3 + 6^3 + 6^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3 + 10^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 6^3 + 9^3 = 2^3 + 3^3 + 5^3 + 5^3 + 6^3 + 6^3 + 6^3 = 3^3 + 3^3 + 3^3 + 3^3 + 5^3 + 7^3 + 7^3.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..343

Crossrefs

Cf. A345526, A345770, A345779, A345781, A345790, A345830.

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 == 8])
    for x in range(len(rets)):
        print(rets[x])