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%I #6 Jul 31 2021 21:28:16
%S 264,279,294,309,324,339,344,359,374,389,404,424,439,454,469,504,549,
%T 564,579,584,614,629,644,664,679,694,709,759,789,804,819,839,854,869,
%U 884,888,903,918,933,934,948,949,968,983,998,1013,1014,1029,1044,1048,1059
%N Numbers that are the sum of nine fourth powers in exactly two ways.
%C Differs from A345586 at term 17 because 519 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 = 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4.
%H Sean A. Irvine, <a href="/A345844/b345844.txt">Table of n, a(n) for n = 1..10000</a>
%e 279 is a term because 279 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4.
%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, 9):
%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. A345586, A345794, A345834, A345843, A345845, A345854, A346337.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 26 2021
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