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A344926 Numbers that are the sum of four fourth powers in nine or more ways.

%I A344926 #6 Jul 31 2021 18:22:23
%S A344926 328118259,385202034,395613234,489597858,592417938,625839858,
%T A344926 641398338,674511618,677125218,693239634,699598578,722302434,
%U A344926 779889314,780278643,780595299,781388643,782999714,791204514,792005379,797405714,797935698,803898018,805299699
%N A344926 Numbers that are the sum of four fourth powers in nine or more ways.
%H A344926 David Consiglio, Jr., <a href="/A344926/b344926.txt">Table of n, a(n) for n = 1..79</a>
%e A344926 328118259 is a term because 328118259 = 2^4 + 77^4 + 109^4 + 111^4  = 8^4 + 79^4 + 93^4 + 121^4  = 18^4 + 79^4 + 97^4 + 119^4  = 21^4 + 77^4 + 98^4 + 119^4  = 27^4 + 77^4 + 94^4 + 121^4  = 34^4 + 77^4 + 89^4 + 123^4  = 46^4 + 57^4 + 103^4 + 119^4  = 49^4 + 77^4 + 77^4 + 126^4  = 61^4 + 66^4 + 77^4 + 127^4.
%o A344926 (Python)
%o A344926 from itertools import combinations_with_replacement as cwr
%o A344926 from collections import defaultdict
%o A344926 keep = defaultdict(lambda: 0)
%o A344926 power_terms = [x**4 for x in range(1, 1000)]
%o A344926 for pos in cwr(power_terms, 4):
%o A344926     tot = sum(pos)
%o A344926     keep[tot] += 1
%o A344926 rets = sorted([k for k, v in keep.items() if v >= 9])
%o A344926 for x in range(len(rets)):
%o A344926     print(rets[x])
%Y A344926 Cf. A341891, A344750, A344924, A344927, A344928, A345146.
%K A344926 nonn
%O A344926 1,1
%A A344926 _David Consiglio, Jr._, Jun 02 2021