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A345857 Numbers that are the sum of ten fourth powers in exactly five ways.

%I A345857 #6 Jul 31 2021 20:00:17
%S A345857 2935,3110,3190,3205,3270,3445,3814,3940,4165,4180,4195,4215,4245,
%T A345857 4260,4290,4310,4325,4375,4420,4435,4615,4660,4675,4695,4774,4805,
%U A345857 4854,4869,4870,4900,4934,4965,4999,5029,5030,5044,5045,5095,5110,5125,5140,5174,5235
%N A345857 Numbers that are the sum of ten fourth powers in exactly five ways.
%C A345857 Differs from A345598 at term 3 because 3175 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 4^4 + 7^4  = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 7^4  = 1^4 + 1^4 + 1^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4  = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4  = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 7^4  = 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4.
%H A345857 Sean A. Irvine, <a href="/A345857/b345857.txt">Table of n, a(n) for n = 1..10000</a>
%e A345857 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 A345857 (Python)
%o A345857 from itertools import combinations_with_replacement as cwr
%o A345857 from collections import defaultdict
%o A345857 keep = defaultdict(lambda: 0)
%o A345857 power_terms = [x**4 for x in range(1, 1000)]
%o A345857 for pos in cwr(power_terms, 10):
%o A345857     tot = sum(pos)
%o A345857     keep[tot] += 1
%o A345857     rets = sorted([k for k, v in keep.items() if v == 5])
%o A345857     for x in range(len(rets)):
%o A345857         print(rets[x])
%Y A345857 Cf. A345598, A345807, A345847, A345856, A345858, A346350.
%K A345857 nonn
%O A345857 1,1
%A A345857 _David Consiglio, Jr._, Jun 26 2021