cp's OEIS Frontend

A345828 Numbers that are the sum of seven fourth powers in exactly six ways.

%I A345828 #6 Jul 31 2021 21:36:53
%S A345828 10787,15396,15411,15586,15651,16611,16626,16676,16866,17956,18867,
%T A345828 19156,19236,19251,19411,19426,19666,20035,20771,21012,21187,21397,
%U A345828 21412,21442,21492,21572,21621,21811,21891,22116,22132,22292,22307,22372,22595,22660,22962
%N A345828 Numbers that are the sum of seven fourth powers in exactly six ways.
%C A345828 Differs from A345572 at term 9 because 16691 = 1^4 + 1^4 + 1^4 + 6^4 + 6^4 + 8^4 + 10^4  = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4 + 10^4  = 1^4 + 2^4 + 5^4 + 6^4 + 8^4 + 8^4 + 9^4  = 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 6^4 + 11^4  = 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 + 10^4  = 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 10^4  = 3^4 + 5^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4.
%H A345828 Sean A. Irvine, <a href="/A345828/b345828.txt">Table of n, a(n) for n = 1..10000</a>
%e A345828 15396 is a term because 15396 = 1^4 + 1^4 + 1^4 + 1^4 + 6^4 + 8^4 + 10^4 = 1^4 + 1^4 + 2^4 + 5^4 + 8^4 + 8^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 11^4 = 1^4 + 3^4 + 4^4 + 4^4 + 7^4 + 7^4 + 10^4 = 1^4 + 3^4 + 5^4 + 7^4 + 8^4 + 8^4 + 8^4 = 2^4 + 3^4 + 4^4 + 5^4 + 6^4 + 9^4 + 9^4.
%o A345828 (Python)
%o A345828 from itertools import combinations_with_replacement as cwr
%o A345828 from collections import defaultdict
%o A345828 keep = defaultdict(lambda: 0)
%o A345828 power_terms = [x**4 for x in range(1, 1000)]
%o A345828 for pos in cwr(power_terms, 7):
%o A345828     tot = sum(pos)
%o A345828     keep[tot] += 1
%o A345828     rets = sorted([k for k, v in keep.items() if v == 6])
%o A345828     for x in range(len(rets)):
%o A345828         print(rets[x])
%Y A345828 Cf. A345572, A345778, A345818, A345827, A345829, A345838, A346283.
%K A345828 nonn
%O A345828 1,1
%A A345828 _David Consiglio, Jr._, Jun 26 2021