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

1,1

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.

Links

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

Example

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.

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, 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])

Crossrefs

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

Sequence in context: A029819 A336192 A345526 * A302900 A317284 A060062

Adjacent sequences: A345777 A345778 A345779 * A345781 A345782 A345783

Keyword

nonn

Author

David Consiglio, Jr., Jun 26 2021

Status

approved