A344738 - OEIS

%I #16 Jul 29 2023 13:57:13

%S 5745705602,8185089458,11054952818,14355295682,21789116258,

%T 22247419922,26839201298,29428835618,31861462178,37314202562,

%U 38214512882,41923075922,46543615202,51711350418,54438780578,56255300738,59223741122,62862779042,63429959138,71035097042

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

%C 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 David Consiglio, Jr., <a href="/A344738/b344738.txt">Table of n, a(n) for n = 1..100</a>

%e 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 (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**4 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 3):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v == 8])

%o for x in range(len(rets)):

%o     print(rets[x])

%Y Cf. A344730, A344737, A344751, A344925, A345088.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, May 27 2021