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A345845 Numbers that are the sum of nine fourth powers in exactly three ways.

%I A345845 #6 Jul 31 2021 21:28:19
%S A345845 519,534,599,774,1143,1364,1539,1604,1619,1814,2579,2644,2659,2679,
%T A345845 2694,2709,2724,2739,2754,2759,2774,2789,2819,2834,2839,2869,2884,
%U A345845 2899,2994,2999,3079,3109,3124,3139,3303,3318,3333,3334,3363,3364,3379,3383,3398,3463
%N A345845 Numbers that are the sum of nine fourth powers in exactly three ways.
%C A345845 Differs from A345587 at term 26 because 285.
%H A345845 Sean A. Irvine, <a href="/A345845/b345845.txt">Table of n, a(n) for n = 1..10000</a>
%e A345845 534 is a term because 534 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 4^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4.
%o A345845 (Python)
%o A345845 from itertools import combinations_with_replacement as cwr
%o A345845 from collections import defaultdict
%o A345845 keep = defaultdict(lambda: 0)
%o A345845 power_terms = [x**4 for x in range(1, 1000)]
%o A345845 for pos in cwr(power_terms, 9):
%o A345845     tot = sum(pos)
%o A345845     keep[tot] += 1
%o A345845     rets = sorted([k for k, v in keep.items() if v == 3])
%o A345845     for x in range(len(rets)):
%o A345845         print(rets[x])
%Y A345845 Cf. A345587, A345795, A345835, A345844, A345846, A345855, A346338.
%K A345845 nonn
%O A345845 1,1
%A A345845 _David Consiglio, Jr._, Jun 26 2021