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A345577 Numbers that are the sum of eight fourth powers in two or more ways.

%I A345577 #6 Jul 31 2021 17:51:26
%S A345577 263,278,293,308,323,343,358,373,388,423,438,453,503,518,533,548,563,
%T A345577 583,598,613,628,678,693,758,773,788,803,853,868,887,902,917,932,933,
%U A345577 967,982,997,1028,1043,1047,1062,1108,1127,1142,1157,1172,1222,1237,1283
%N A345577 Numbers that are the sum of eight fourth powers in two or more ways.
%H A345577 Sean A. Irvine, <a href="/A345577/b345577.txt">Table of n, a(n) for n = 1..10000</a>
%e A345577 278 is a term because 278 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4.
%o A345577 (Python)
%o A345577 from itertools import combinations_with_replacement as cwr
%o A345577 from collections import defaultdict
%o A345577 keep = defaultdict(lambda: 0)
%o A345577 power_terms = [x**4 for x in range(1, 1000)]
%o A345577 for pos in cwr(power_terms, 8):
%o A345577     tot = sum(pos)
%o A345577     keep[tot] += 1
%o A345577     rets = sorted([k for k, v in keep.items() if v >= 2])
%o A345577     for x in range(len(rets)):
%o A345577         print(rets[x])
%Y A345577 Cf. A003342, A345532, A345568, A345578, A345586, A345610, A345834.
%K A345577 nonn
%O A345577 1,1
%A A345577 _David Consiglio, Jr._, Jun 20 2021