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A345838 Numbers that are the sum of eight fourth powers in exactly six ways.

%I A345838 #6 Jul 31 2021 21:33:41
%S A345838 6723,6788,6853,6898,6963,7028,7938,8068,8178,8308,8483,8963,9173,
%T A345838 9348,9413,9493,9668,9763,9828,10003,10132,10258,10277,10307,10628,
%U A345838 10708,10738,10788,10933,10978,11108,11123,11188,11347,11363,11428,11492,11652,11668,11843
%N A345838 Numbers that are the sum of eight fourth powers in exactly six ways.
%C A345838 Differs from A345581 at term 8 because 8003 = 1^4 + 1^4 + 1^4 + 2^4 + 6^4 + 6^4 + 6^4 + 8^4  = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 6^4 + 9^4  = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 6^4 + 7^4 + 8^4  = 2^4 + 2^4 + 4^4 + 4^4 + 4^4 + 7^4 + 7^4 + 7^4  = 2^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4 + 7^4 + 7^4  = 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 9^4  = 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 6^4 + 7^4.
%H A345838 Sean A. Irvine, <a href="/A345838/b345838.txt">Table of n, a(n) for n = 1..10000</a>
%e A345838 6788 is a term because 6788 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 4^4 + 7^4 + 8^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 6^4 + 6^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 9^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 7^4 + 8^4 = 2^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4.
%o A345838 (Python)
%o A345838 from itertools import combinations_with_replacement as cwr
%o A345838 from collections import defaultdict
%o A345838 keep = defaultdict(lambda: 0)
%o A345838 power_terms = [x**4 for x in range(1, 1000)]
%o A345838 for pos in cwr(power_terms, 8):
%o A345838     tot = sum(pos)
%o A345838     keep[tot] += 1
%o A345838     rets = sorted([k for k, v in keep.items() if v == 6])
%o A345838     for x in range(len(rets)):
%o A345838         print(rets[x])
%Y A345838 Cf. A345581, A345788, A345828, A345837, A345839, A345848, A346331.
%K A345838 nonn
%O A345838 1,1
%A A345838 _David Consiglio, Jr._, Jun 26 2021