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A345586 Numbers that are the sum of nine fourth powers in two or more ways.

%I A345586 #6 Jul 31 2021 17:38:42
%S A345586 264,279,294,309,324,339,344,359,374,389,404,424,439,454,469,504,519,
%T A345586 534,549,564,579,584,599,614,629,644,664,679,694,709,759,774,789,804,
%U A345586 819,839,854,869,884,888,903,918,933,934,948,949,968,983,998,1013,1014
%N A345586 Numbers that are the sum of nine fourth powers in two or more ways.
%H A345586 Sean A. Irvine, <a href="/A345586/b345586.txt">Table of n, a(n) for n = 1..10000</a>
%e A345586 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 A345586 (Python)
%o A345586 from itertools import combinations_with_replacement as cwr
%o A345586 from collections import defaultdict
%o A345586 keep = defaultdict(lambda: 0)
%o A345586 power_terms = [x**4 for x in range(1, 1000)]
%o A345586 for pos in cwr(power_terms, 9):
%o A345586     tot = sum(pos)
%o A345586     keep[tot] += 1
%o A345586     rets = sorted([k for k, v in keep.items() if v >= 2])
%o A345586     for x in range(len(rets)):
%o A345586         print(rets[x])
%Y A345586 Cf. A003343, A345541, A345577, A345587, A345595, A345619, A345844.
%K A345586 nonn
%O A345586 1,1
%A A345586 _David Consiglio, Jr._, Jun 20 2021