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 A345774 Numbers that are the sum of seven cubes in exactly two ways. 7

%I #6 Jul 31 2021 22:39:11

%S 131,159,166,173,185,192,211,236,243,257,264,269,274,276,288,290,292,

%T 295,299,300,302,307,309,311,314,320,321,325,332,333,337,339,340,344,

%U 348,351,353,355,358,359,360,363,372,384,385,386,388,389,393,395,398,403

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

%C Differs from A345520 at term 8 because 222 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 6^3 = 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 4^3 = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3 + 5^3.

%C Likely finite.

%H Sean A. Irvine, <a href="/A345774/b345774.txt">Table of n, a(n) for n = 1..355</a>

%e 159 is a term because 159 = 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3.

%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 == 2])

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

%o print(rets[x])

%Y Cf. A048930, A345520, A345773, A345775, A345784, A345824.

%K nonn

%O 1,1

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

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Last modified August 4 16:18 EDT 2024. Contains 374923 sequences. (Running on oeis4.)