cp's OEIS Frontend

A345858 Numbers that are the sum of ten fourth powers in exactly six ways.

%I A345858 #6 Jul 31 2021 20:00:20
%S A345858 3175,4150,4230,4390,4405,4455,4470,4500,4550,4565,4630,4725,4740,
%T A345858 4915,4980,5094,5109,5155,5190,5205,5220,5270,5285,5350,5365,5395,
%U A345858 5430,5475,5635,5655,5735,5910,5955,6020,6069,6084,6149,6195,6214,6324,6389,6435,6500
%N A345858 Numbers that are the sum of ten fourth powers in exactly six ways.
%C A345858 Differs from A345599 at term 8 because 4485 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 8^4  = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 4^4 + 4^4 + 6^4 + 7^4  = 1^4 + 1^4 + 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4  = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 8^4  = 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4  = 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4  = 2^4 + 2^4 + 2^4 + 2^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4 + 6^4.
%H A345858 Sean A. Irvine, <a href="/A345858/b345858.txt">Table of n, a(n) for n = 1..9982</a>
%e A345858 4150 is a term because 4150 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 8^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 + 6^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 7^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 = 1^4 + 4^4 + 4^4 + 4^4 + 4^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 7^4.
%o A345858 (Python)
%o A345858 from itertools import combinations_with_replacement as cwr
%o A345858 from collections import defaultdict
%o A345858 keep = defaultdict(lambda: 0)
%o A345858 power_terms = [x**4 for x in range(1, 1000)]
%o A345858 for pos in cwr(power_terms, 10):
%o A345858     tot = sum(pos)
%o A345858     keep[tot] += 1
%o A345858     rets = sorted([k for k, v in keep.items() if v == 6])
%o A345858     for x in range(len(rets)):
%o A345858         print(rets[x])
%Y A345858 Cf. A345599, A345808, A345848, A345857, A345859, A346351.
%K A345858 nonn
%O A345858 1,1
%A A345858 _David Consiglio, Jr._, Jun 26 2021