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A344737 Numbers that are the sum of three fourth powers in eight or more ways.

%I A344737 #10 Jul 31 2021 18:29:22
%S A344737 5745705602,8185089458,11054952818,14355295682,21789116258,
%T A344737 22247419922,26839201298,29428835618,31861462178,37314202562,
%U A344737 38214512882,41923075922,46543615202,49511121842,51711350418,54438780578,56255300738,59223741122,62862779042,63429959138
%N A344737 Numbers that are the sum of three fourth powers in eight or more ways.
%H A344737 David Consiglio, Jr., <a href="/A344737/b344737.txt">Table of n, a(n) for n = 1..100</a>
%e A344737 5745705602 is a term because 5745705602 = 3^4 + 230^4 + 233^4 = 25^4 + 218^4 + 243^4 = 43^4 + 207^4 + 250^4 = 58^4 + 197^4 + 255^4 = 85^4 + 177^4 + 262^4 = 90^4 + 173^4 + 263^4 = 102^4 + 163^4 + 265^4 = 122^4 + 145^4 + 267^4.
%o A344737 (Python)
%o A344737 from itertools import combinations_with_replacement as cwr
%o A344737 from collections import defaultdict
%o A344737 keep = defaultdict(lambda: 0)
%o A344737 power_terms = [x**4 for x in range(1, 1000)]
%o A344737 for pos in cwr(power_terms, 3):
%o A344737     tot = sum(pos)
%o A344737     keep[tot] += 1
%o A344737 rets = sorted([k for k, v in keep.items() if v >= 8])
%o A344737 for x in range(len(rets)):
%o A344737     print(rets[x])
%Y A344737 Cf. A344729, A344738, A344750, A344924, A345087.
%K A344737 nonn
%O A344737 1,1
%A A344737 _David Consiglio, Jr._, May 27 2021