cp's OEIS Frontend

A345850 Numbers that are the sum of nine fourth powers in exactly eight ways.

%I A345850 #6 Jul 31 2021 21:28:34
%S A345850 6804,6869,8019,8084,8324,8499,8564,9044,9124,9219,9234,9284,9364,
%T A345850 9429,9474,9494,9604,9669,9749,9779,10148,10259,10293,10339,10388,
%U A345850 10453,10514,10579,10628,10644,10754,10789,11029,11059,11189,11204,11299,11363,11364,11379
%N A345850 Numbers that are the sum of nine fourth powers in exactly eight ways.
%C A345850 Differs from A345592 at term 5 because 8259 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 8^4 + 8^4  = 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 6^4 + 6^4 + 6^4 + 8^4  = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 6^4 + 9^4  = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 7^4 + 8^4  = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 8^4  = 2^4 + 2^4 + 4^4 + 4^4 + 4^4 + 4^4 + 7^4 + 7^4 + 7^4  = 2^4 + 3^4 + 4^4 + 4^4 + 4^4 + 6^4 + 6^4 + 7^4 + 7^4  = 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 9^4  = 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4 + 6^4 + 7^4.
%H A345850 Sean A. Irvine, <a href="/A345850/b345850.txt">Table of n, a(n) for n = 1..10000</a>
%e A345850 6869 is a term because 6869 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 9^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 4^4 + 7^4 + 8^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 6^4 + 6^4 + 8^4 = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 9^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 7^4 + 8^4 = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4.
%o A345850 (Python)
%o A345850 from itertools import combinations_with_replacement as cwr
%o A345850 from collections import defaultdict
%o A345850 keep = defaultdict(lambda: 0)
%o A345850 power_terms = [x**4 for x in range(1, 1000)]
%o A345850 for pos in cwr(power_terms, 9):
%o A345850     tot = sum(pos)
%o A345850     keep[tot] += 1
%o A345850     rets = sorted([k for k, v in keep.items() if v == 8])
%o A345850     for x in range(len(rets)):
%o A345850         print(rets[x])
%Y A345850 Cf. A345592, A345800, A345840, A345849, A345851, A345860, A346343.
%K A345850 nonn
%O A345850 1,1
%A A345850 _David Consiglio, Jr._, Jun 26 2021