cp's OEIS Frontend

A345820 Numbers that are the sum of six fourth powers in exactly eight ways.

%I A345820 #6 Jul 31 2021 21:57:32
%S A345820 58035,59780,87746,96195,96450,102371,106451,106515,108035,108275,
%T A345820 108290,108771,112370,112931,115251,122835,122850,124691,125971,
%U A345820 133395,133571,133586,134675,136931,138275,138595,143650,144755,145826,147491,148820,149571,150115
%N A345820 Numbers that are the sum of six fourth powers in exactly eight ways.
%C A345820 Differs from A345565 at term 4 because 88595 = 1^4 + 4^4 + 5^4 + 12^4 + 13^4 + 14^4  = 1^4 + 6^4 + 6^4 + 11^4 + 12^4 + 15^4  = 1^4 + 7^4 + 8^4 + 9^4 + 10^4 + 16^4  = 2^4 + 8^4 + 9^4 + 9^4 + 12^4 + 15^4  = 2^4 + 10^4 + 11^4 + 11^4 + 12^4 + 13^4  = 4^4 + 6^4 + 6^4 + 9^4 + 13^4 + 15^4  = 5^4 + 6^4 + 7^4 + 8^4 + 11^4 + 16^4  = 7^4 + 7^4 + 10^4 + 11^4 + 12^4 + 14^4.
%H A345820 Sean A. Irvine, <a href="/A345820/b345820.txt">Table of n, a(n) for n = 1..10000</a>
%e A345820 59780 is a term because 59780 = 1^4 + 1^4 + 1^4 + 5^4 + 12^4 + 14^4 = 1^4 + 1^4 + 6^4 + 6^4 + 9^4 + 15^4 = 1^4 + 2^4 + 9^4 + 10^4 + 11^4 + 13^4 = 1^4 + 4^4 + 7^4 + 7^4 + 8^4 + 15^4 = 1^4 + 7^4 + 7^4 + 9^4 + 10^4 + 14^4 = 2^4 + 5^4 + 6^4 + 11^4 + 11^4 + 13^4 = 3^4 + 7^4 + 8^4 + 10^4 + 11^4 + 13^4 = 5^4 + 6^4 + 7^4 + 7^4 + 11^4 + 14^4.
%o A345820 (Python)
%o A345820 from itertools import combinations_with_replacement as cwr
%o A345820 from collections import defaultdict
%o A345820 keep = defaultdict(lambda: 0)
%o A345820 power_terms = [x**4 for x in range(1, 1000)]
%o A345820 for pos in cwr(power_terms, 6):
%o A345820     tot = sum(pos)
%o A345820     keep[tot] += 1
%o A345820     rets = sorted([k for k, v in keep.items() if v == 8])
%o A345820     for x in range(len(rets)):
%o A345820         print(rets[x])
%Y A345820 Cf. A344945, A345565, A345770, A345819, A345821, A345830, A346363.
%K A345820 nonn
%O A345820 1,1
%A A345820 _David Consiglio, Jr._, Jun 26 2021