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%I #6 Jul 31 2021 21:36:50
%S 6642,6707,6772,6882,6947,7922,7987,8227,8962,9267,9507,9747,10116,
%T 10291,10722,10867,10932,10962,11331,11411,11571,12676,12851,12916,
%U 13187,13252,13891,13956,14131,14211,14707,14772,14802,14917,14932,14947,15012,15092,15316
%N Numbers that are the sum of seven fourth powers in exactly five ways.
%C Differs from A345571 at term 16 because 10787 = 1^4 + 1^4 + 1^4 + 6^4 + 6^4 + 8^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 8^4 + 9^4 = 1^4 + 2^4 + 4^4 + 4^4 + 6^4 + 7^4 + 9^4 = 1^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 9^4 = 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 + 8^4 = 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 8^4.
%H Sean A. Irvine, <a href="/A345827/b345827.txt">Table of n, a(n) for n = 1..10000</a>
%e 6707 is a term because 6707 = 1^4 + 1^4 + 1^4 + 2^4 + 6^4 + 6^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 = 2^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4.
%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**4 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 == 5])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A345571, A345777, A345817, A345826, A345828, A345837, A346282.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 26 2021
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