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A344738 Numbers that are the sum of three fourth powers in exactly eight ways.

%I A344738 #16 Jul 29 2023 13:57:13
%S A344738 5745705602,8185089458,11054952818,14355295682,21789116258,
%T A344738 22247419922,26839201298,29428835618,31861462178,37314202562,
%U A344738 38214512882,41923075922,46543615202,51711350418,54438780578,56255300738,59223741122,62862779042,63429959138,71035097042
%N A344738 Numbers that are the sum of three fourth powers in exactly eight ways.
%C A344738 Differs at term 14 because 49511121842 = 13^4 + 390^4 + 403^4 = 35^4 + 378^4 + 413^4 = 70^4 + 357^4 + 427^4 = 103^4 + 335^4 + 438^4 = 117^4 + 325^4 + 442^4 = 137^4 + 310^4 + 447^4 = 175^4 + 322^4 + 441^4 = 182^4 + 273^4 + 455^4 = 202^4 + 255^4 + 457^4 = 225^4 + 233^4 + 458^4.
%H A344738 David Consiglio, Jr., <a href="/A344738/b344738.txt">Table of n, a(n) for n = 1..100</a>
%e A344738 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 A344738 (Python)
%o A344738 from itertools import combinations_with_replacement as cwr
%o A344738 from collections import defaultdict
%o A344738 keep = defaultdict(lambda: 0)
%o A344738 power_terms = [x**4 for x in range(1, 1000)]
%o A344738 for pos in cwr(power_terms, 3):
%o A344738     tot = sum(pos)
%o A344738     keep[tot] += 1
%o A344738 rets = sorted([k for k, v in keep.items() if v == 8])
%o A344738 for x in range(len(rets)):
%o A344738     print(rets[x])
%Y A344738 Cf. A344730, A344737, A344751, A344925, A345088.
%K A344738 nonn
%O A344738 1,1
%A A344738 _David Consiglio, Jr._, May 27 2021