cp's OEIS Frontend

A345848 Numbers that are the sum of nine fourth powers in exactly six ways.

%I A345848 #6 Jul 31 2021 21:28:28
%S A345848 4469,4484,5444,5459,5524,5589,5699,5764,6629,6659,6674,6694,6724,
%T A345848 6789,6884,6899,6914,6934,6949,6964,7014,7154,7219,7334,7348,7349,
%U A345848 7413,7459,7478,7494,7523,7524,7588,7589,7604,7653,7669,7734,7779,7874,7954,7989,8069
%N A345848 Numbers that are the sum of nine fourth powers in exactly six ways.
%C A345848 Differs from A345590 at term 14 because 6739 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 6^4 + 6^4 + 8^4  = 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4  = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4  = 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4  = 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4  = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4  = 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4.
%H A345848 Sean A. Irvine, <a href="/A345848/b345848.txt">Table of n, a(n) for n = 1..10000</a>
%e A345848 4484 is a term because 4484 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 8^4 = 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 4^4 + 4^4 + 6^4 + 7^4 = 1^4 + 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4 = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 8^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4.
%o A345848 (Python)
%o A345848 from itertools import combinations_with_replacement as cwr
%o A345848 from collections import defaultdict
%o A345848 keep = defaultdict(lambda: 0)
%o A345848 power_terms = [x**4 for x in range(1, 1000)]
%o A345848 for pos in cwr(power_terms, 9):
%o A345848     tot = sum(pos)
%o A345848     keep[tot] += 1
%o A345848     rets = sorted([k for k, v in keep.items() if v == 6])
%o A345848     for x in range(len(rets)):
%o A345848         print(rets[x])
%Y A345848 Cf. A345590, A345798, A345838, A345847, A345849, A345858, A346341.
%K A345848 nonn
%O A345848 1,1
%A A345848 _David Consiglio, Jr._, Jun 26 2021