cp's OEIS Frontend

A345822 Numbers that are the sum of six fourth powers in exactly ten ways.

%I A345822 #6 Jul 31 2021 21:57:40
%S A345822 122915,151556,161475,162755,173075,183620,185315,199106,199940,
%T A345822 201875,202275,204275,204340,204595,206115,207395,209795,211075,
%U A345822 213731,217826,217891,218515,221250,223955,224180,225875,226595,227186,228035,236195,237796,237890
%N A345822 Numbers that are the sum of six fourth powers in exactly ten ways.
%C A345822 Differs from A345567 at term 8 because 197795 = 1^4 + 2^4 + 5^4 + 6^4 + 16^4 + 19^4  = 1^4 + 2^4 + 7^4 + 11^4 + 12^4 + 20^4  = 1^4 + 2^4 + 10^4 + 12^4 + 17^4 + 17^4  = 2^4 + 4^4 + 7^4 + 9^4 + 13^4 + 20^4  = 2^4 + 11^4 + 13^4 + 14^4 + 15^4 + 16^4  = 3^4 + 6^4 + 6^4 + 9^4 + 13^4 + 20^4  = 3^4 + 6^4 + 7^4 + 14^4 + 15^4 + 18^4  = 4^4 + 9^4 + 11^4 + 12^4 + 15^4 + 18^4  = 7^4 + 7^4 + 14^4 + 14^4 + 15^4 + 16^4.
%H A345822 Sean A. Irvine, <a href="/A345822/b345822.txt">Table of n, a(n) for n = 1..10000</a>
%e A345822 151556 is a term because 151556 = 1^4 + 2^4 + 2^4 + 9^4 + 11^4 + 19^4 = 1^4 + 2^4 + 3^4 + 7^4 + 16^4 + 17^4 = 1^4 + 8^4 + 11^4 + 12^4 + 13^4 + 17^4 = 2^4 + 3^4 + 7^4 + 8^4 + 11^4 + 19^4 = 3^4 + 3^4 + 3^4 + 4^4 + 12^4 + 19^4 = 3^4 + 4^4 + 11^4 + 11^4 + 14^4 + 17^4 = 3^4 + 4^4 + 13^4 + 13^4 + 13^4 + 16^4 = 4^4 + 6^4 + 9^4 + 9^4 + 9^4 + 19^4 = 4^4 + 7^4 + 11^4 + 11^4 + 11^4 + 18^4 = 4^4 + 8^4 + 9^4 + 13^4 + 13^4 + 17^4.
%o A345822 (Python)
%o A345822 from itertools import combinations_with_replacement as cwr
%o A345822 from collections import defaultdict
%o A345822 keep = defaultdict(lambda: 0)
%o A345822 power_terms = [x**4 for x in range(1, 1000)]
%o A345822 for pos in cwr(power_terms, 6):
%o A345822     tot = sum(pos)
%o A345822     keep[tot] += 1
%o A345822     rets = sorted([k for k, v in keep.items() if v == 10])
%o A345822     for x in range(len(rets)):
%o A345822         print(rets[x])
%Y A345822 Cf. A341898, A345567, A345772, A345821, A345832, A346365.
%K A345822 nonn
%O A345822 1,1
%A A345822 _David Consiglio, Jr._, Jun 26 2021