A345780 - OEIS

%I #6 Jul 31 2021 22:39:30

%S 1385,1515,1552,1557,1585,1587,1603,1613,1622,1655,1665,1674,1681,

%T 1718,1719,1739,1741,1746,1753,1755,1765,1767,1782,1793,1805,1809,

%U 1811,1818,1819,1826,1828,1830,1833,1838,1856,1870,1873,1881,1901,1905,1931,1935,1937

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

%C 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.

%C Likely finite.

%H Sean A. Irvine, <a href="/A345780/b345780.txt">Table of n, a(n) for n = 1..343</a>

%e 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.

%o (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**3 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 7):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o     rets = sorted([k for k, v in keep.items() if v == 8])

%o     for x in range(len(rets)):

%o         print(rets[x])

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

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 26 2021