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A345839 Numbers that are the sum of eight fourth powers in exactly seven ways.

%I A345839 #6 Jul 31 2021 21:33:44
%S A345839 8003,8243,9043,9218,9283,9523,10372,10803,10868,10948,11043,11412,
%T A345839 11557,11587,12083,12692,12932,13188,13333,13508,13972,14147,14387,
%U A345839 14883,14933,14948,14963,15013,15028,15093,15173,15268,15317,15332,15397,15412,15413,15492
%N A345839 Numbers that are the sum of eight fourth powers in exactly seven ways.
%C A345839 Differs from A345582 at term 19 because 13268 = 1^4 + 1^4 + 1^4 + 2^4 + 6^4 + 6^4 + 8^4 + 9^4  = 1^4 + 1^4 + 2^4 + 4^4 + 7^4 + 7^4 + 8^4 + 8^4  = 1^4 + 1^4 + 3^4 + 6^4 + 6^4 + 7^4 + 8^4 + 8^4  = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4 + 9^4  = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 + 9^4  = 2^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 9^4  = 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 + 9^4  = 4^4 + 4^4 + 4^4 + 5^4 + 5^4 + 5^4 + 5^4 + 10^4.
%H A345839 Sean A. Irvine, <a href="/A345839/b345839.txt">Table of n, a(n) for n = 1..10000</a>
%e A345839 8243 is a term because 8243 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 8^4 + 8^4 = 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 + 6^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 6^4 + 9^4 = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 7^4 + 8^4 = 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 8^4 = 2^4 + 4^4 + 4^4 + 4^4 + 4^4 + 7^4 + 7^4 + 7^4 = 3^4 + 4^4 + 4^4 + 4^4 + 6^4 + 6^4 + 7^4 + 7^4.
%o A345839 (Python)
%o A345839 from itertools import combinations_with_replacement as cwr
%o A345839 from collections import defaultdict
%o A345839 keep = defaultdict(lambda: 0)
%o A345839 power_terms = [x**4 for x in range(1, 1000)]
%o A345839 for pos in cwr(power_terms, 8):
%o A345839     tot = sum(pos)
%o A345839     keep[tot] += 1
%o A345839     rets = sorted([k for k, v in keep.items() if v == 7])
%o A345839     for x in range(len(rets)):
%o A345839         print(rets[x])
%Y A345839 Cf. A345582, A345789, A345829, A345838, A345840, A345849, A346332.
%K A345839 nonn
%O A345839 1,1
%A A345839 _David Consiglio, Jr._, Jun 26 2021