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 A345638 Numbers that are the sum of ten fifth powers in six or more ways. 6

%I #6 Jul 31 2021 15:58:41

%S 392095,392306,399839,406802,407583,434676,491643,492063,520261,

%T 521106,538323,538534,540927,553325,555098,563526,582089,592398,

%U 608190,611072,614196,637833,639903,640715,640895,640926,640957,641106,643671,653523,655327,656616

%N Numbers that are the sum of ten fifth powers in six or more ways.

%H Sean A. Irvine, <a href="/A345638/b345638.txt">Table of n, a(n) for n = 1..10000</a>

%e 392306 is a term because 392306 = 1^5 + 1^5 + 1^5 + 3^5 + 3^5 + 8^5 + 9^5 + 10^5 + 10^5 + 10^5 = 1^5 + 1^5 + 2^5 + 4^5 + 4^5 + 7^5 + 8^5 + 8^5 + 9^5 + 12^5 = 1^5 + 2^5 + 3^5 + 3^5 + 4^5 + 5^5 + 8^5 + 8^5 + 11^5 + 11^5 = 2^5 + 2^5 + 3^5 + 3^5 + 3^5 + 6^5 + 7^5 + 9^5 + 9^5 + 12^5 = 2^5 + 2^5 + 3^5 + 4^5 + 4^5 + 4^5 + 6^5 + 9^5 + 11^5 + 11^5 = 2^5 + 2^5 + 3^5 + 4^5 + 5^5 + 5^5 + 5^5 + 8^5 + 10^5 + 12^5.

%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**5 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 10):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v >= 6])

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

%o print(rets[x])

%Y Cf. A345599, A345623, A345637, A345639, A346351.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 20 2021

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Last modified February 26 17:57 EST 2024. Contains 370352 sequences. (Running on oeis4.)