A345779 Numbers that are the sum of seven cubes in exactly seven ways.

1072, 1170, 1235, 1261, 1268, 1305, 1392, 1396, 1411, 1440, 1441, 1448, 1450, 1459, 1489, 1502, 1504, 1513, 1538, 1540, 1547, 1559, 1564, 1565, 1566, 1567, 1576, 1592, 1593, 1594, 1600, 1602, 1606, 1620, 1621, 1625, 1626, 1628, 1629, 1639, 1658, 1664, 1667

Offset: 1

Author

David Consiglio, Jr., Jun 26 2021

Keywords

• nonn

Comments

Differs from A345525 at term 7 because 1385 = 1^3 + 1^3 + 2^3 + 2^3 + 7^3 + 8^3 + 8^3 = 1^3 + 1^3 + 2^3 + 5^3 + 5^3 + 5^3 + 10^3 = 1^3 + 2^3 + 2^3 + 3^3 + 5^3 + 6^3 + 10^3 = 1^3 + 2^3 + 6^3 + 6^3 + 6^3 + 6^3 + 8^3 = 1^3 + 4^3 + 5^3 + 5^3 + 5^3 + 6^3 + 9^3 = 2^3 + 3^3 + 3^3 + 5^3 + 7^3 + 7^3 + 8^3 = 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 6^3 + 9^3 = 3^3 + 3^3 + 3^3 + 4^3 + 6^3 + 8^3 + 8^3.

Likely finite.

Examples

			1170 is a term because 1170 = 1^3 + 1^3 + 2^3 + 2^3 + 3^3 + 4^3 + 9^3 = 1^3 + 1^3 + 2^3 + 5^3 + 5^3 + 5^3 + 7^3 = 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 4^3 + 8^3 = 1^3 + 2^3 + 3^3 + 3^3 + 4^3 + 5^3 + 8^3 = 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 7^3 + 7^3 = 3^3 + 3^3 + 4^3 + 5^3 + 5^3 + 5^3 + 6^3 = 3^3 + 3^3 + 3^3 + 4^3 + 4^3 + 5^3 + 7^3.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..345

Crossrefs

Cf. A345525, A345769, A345778, A345780, A345789, A345829.

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 == 7])
    for x in range(len(rets)):
        print(rets[x])