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 A345776 Numbers that are the sum of seven cubes in exactly four ways. 7

%I #6 Jul 31 2021 22:39:17

%S 470,496,503,603,634,653,659,685,690,692,711,712,747,751,754,761,766,

%T 773,775,777,780,783,787,792,794,812,813,829,831,836,842,843,859,867,

%U 871,875,883,885,890,892,899,901,904,906,907,911,913,918,919,927,930,936

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

%C Differs from A345522 at term 5 because 627 = 1^3 + 1^3 + 1^3 + 1^3 + 4^3 + 6^3 + 7^3 = 1^3 + 1^3 + 5^3 + 5^3 + 5^3 + 5^3 + 5^3 = 1^3 + 2^3 + 3^3 + 5^3 + 5^3 + 5^3 + 6^3 = 1^3 + 3^3 + 4^3 + 4^3 + 4^3 + 4^3 + 7^3 = 2^3 + 2^3 + 3^3 + 3^3 + 5^3 + 6^3 + 6^3.

%C Likely finite.

%H Sean A. Irvine, <a href="/A345776/b345776.txt">Table of n, a(n) for n = 1..360</a>

%e 496 is a term because 496 = 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 5^3 = 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 5^3 + 5^3 = 1^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 6^3 = 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 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 == 4])

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

%o print(rets[x])

%Y Cf. A345522, A345766, A345775, A345777, A345786, A345826.

%K nonn

%O 1,1

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

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Last modified September 10 08:45 EDT 2024. Contains 375786 sequences. (Running on oeis4.)