cp's OEIS Frontend

A345782 Numbers that are the sum of seven cubes in exactly ten ways.

%I A345782 #6 Jul 31 2021 22:39:38
%S A345782 1704,1711,1800,1837,1863,1926,1938,1963,2008,2019,2045,2053,2059,
%T A345782 2078,2113,2143,2161,2171,2176,2217,2223,2250,2260,2266,2276,2286,
%U A345782 2295,2304,2313,2315,2331,2350,2354,2357,2374,2404,2412,2413,2442,2444,2446,2447,2511
%N A345782 Numbers that are the sum of seven cubes in exactly ten ways.
%C A345782 Differs from A345506 at term 3 because 1774 = 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 3^3 + 12^3  = 1^3 + 1^3 + 1^3 + 2^3 + 6^3 + 6^3 + 11^3  = 1^3 + 1^3 + 2^3 + 2^3 + 3^3 + 9^3 + 10^3  = 1^3 + 1^3 + 4^3 + 5^3 + 5^3 + 9^3 + 9^3  = 1^3 + 2^3 + 3^3 + 4^3 + 6^3 + 9^3 + 9^3  = 1^3 + 2^3 + 4^3 + 4^3 + 5^3 + 8^3 + 10^3  = 1^3 + 4^3 + 4^3 + 4^3 + 5^3 + 5^3 + 11^3  = 2^3 + 2^3 + 2^3 + 4^3 + 7^3 + 7^3 + 10^3  = 2^3 + 3^3 + 4^3 + 4^3 + 4^3 + 6^3 + 11^3  = 3^3 + 3^3 + 6^3 + 6^3 + 6^3 + 7^3 + 9^3  = 4^3 + 4^3 + 4^3 + 5^3 + 6^3 + 8^3 + 9^3.
%C A345782 Likely finite.
%H A345782 Sean A. Irvine, <a href="/A345782/b345782.txt">Table of n, a(n) for n = 1..328</a>
%e A345782 1711 is a term because 1711 = 1^3 + 1^3 + 1^3 + 4^3 + 4^3 + 8^3 + 8^3 = 1^3 + 1^3 + 2^3 + 3^3 + 5^3 + 8^3 + 8^3 = 1^3 + 1^3 + 2^3 + 3^3 + 4^3 + 7^3 + 9^3 = 1^3 + 1^3 + 3^3 + 3^3 + 4^3 + 4^3 + 10^3 = 1^3 + 2^3 + 2^3 + 2^3 + 6^3 + 6^3 + 9^3 = 1^3 + 2^3 + 3^3 + 3^3 + 3^3 + 5^3 + 10^3 = 1^3 + 3^3 + 3^3 + 4^3 + 5^3 + 7^3 + 8^3 = 2^3 + 2^3 + 3^3 + 5^3 + 6^3 + 6^3 + 8^3 = 3^3 + 3^3 + 3^3 + 4^3 + 4^3 + 6^3 + 9^3 = 4^3 + 4^3 + 5^3 + 5^3 + 6^3 + 6^3 + 6^3.
%o A345782 (Python)
%o A345782 from itertools import combinations_with_replacement as cwr
%o A345782 from collections import defaultdict
%o A345782 keep = defaultdict(lambda: 0)
%o A345782 power_terms = [x**3 for x in range(1, 1000)]
%o A345782 for pos in cwr(power_terms, 7):
%o A345782     tot = sum(pos)
%o A345782     keep[tot] += 1
%o A345782     rets = sorted([k for k, v in keep.items() if v == 10])
%o A345782     for x in range(len(rets)):
%o A345782         print(rets[x])
%Y A345782 Cf. A345506, A345772, A345781, A345792, A345832.
%K A345782 nonn
%O A345782 1,1
%A A345782 _David Consiglio, Jr._, Jun 26 2021