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A345598 Numbers that are the sum of ten fourth powers in five or more ways.

%I A345598 #6 Jul 31 2021 17:25:51
%S A345598 2935,3110,3175,3190,3205,3270,3445,3814,3940,4150,4165,4180,4195,
%T A345598 4215,4230,4245,4260,4290,4310,4325,4375,4390,4405,4420,4435,4455,
%U A345598 4470,4485,4500,4550,4565,4615,4630,4660,4675,4695,4725,4740,4774,4805,4854,4869,4870
%N A345598 Numbers that are the sum of ten fourth powers in five or more ways.
%H A345598 Sean A. Irvine, <a href="/A345598/b345598.txt">Table of n, a(n) for n = 1..10000</a>
%e A345598 3110 is a term because 3110 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 6^4 + 6^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 7^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4.
%o A345598 (Python)
%o A345598 from itertools import combinations_with_replacement as cwr
%o A345598 from collections import defaultdict
%o A345598 keep = defaultdict(lambda: 0)
%o A345598 power_terms = [x**4 for x in range(1, 1000)]
%o A345598 for pos in cwr(power_terms, 10):
%o A345598     tot = sum(pos)
%o A345598     keep[tot] += 1
%o A345598     rets = sorted([k for k, v in keep.items() if v >= 5])
%o A345598     for x in range(len(rets)):
%o A345598         print(rets[x])
%Y A345598 Cf. A345553, A345589, A345597, A345599, A345637, A345857.
%K A345598 nonn
%O A345598 1,1
%A A345598 _David Consiglio, Jr._, Jun 20 2021