cp's OEIS Frontend

A345829 Numbers that are the sum of seven fourth powers in exactly seven ways.

%I A345829 #6 Jul 31 2021 21:36:57
%S A345829 16691,17347,17971,20706,21956,22547,22612,23156,23587,23827,23892,
%T A345829 24436,25107,25427,25716,25971,26051,27812,29092,29187,29332,29427,
%U A345829 29442,29636,29701,29716,29956,29971,30036,30132,30612,30981,30996,31011,31316,31331,31347
%N A345829 Numbers that are the sum of seven fourth powers in exactly seven ways.
%C A345829 Differs from A345573 at term 4 because 19491 = 1^4 + 1^4 + 1^4 + 6^4 + 8^4 + 8^4 + 10^4  = 1^4 + 2^4 + 4^4 + 4^4 + 7^4 + 9^4 + 10^4  = 1^4 + 2^4 + 5^4 + 8^4 + 8^4 + 8^4 + 9^4  = 1^4 + 3^4 + 4^4 + 6^4 + 6^4 + 9^4 + 10^4  = 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 8^4 + 11^4  = 2^4 + 4^4 + 4^4 + 5^4 + 6^4 + 7^4 + 11^4  = 3^4 + 4^4 + 4^4 + 7^4 + 7^4 + 8^4 + 10^4  = 3^4 + 4^4 + 5^4 + 6^4 + 6^4 + 6^4 + 11^4  = 3^4 + 5^4 + 7^4 + 8^4 + 8^4 + 8^4 + 8^4.
%H A345829 Sean A. Irvine, <a href="/A345829/b345829.txt">Table of n, a(n) for n = 1..10000</a>
%e A345829 17347 is a term because 17347 = 1^4 + 1^4 + 6^4 + 6^4 + 8^4 + 8^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 11^4 = 1^4 + 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 11^4 = 1^4 + 4^4 + 7^4 + 7^4 + 8^4 + 8^4 + 8^4 = 2^4 + 2^4 + 2^4 + 3^4 + 8^4 + 9^4 + 9^4 = 2^4 + 4^4 + 4^4 + 6^4 + 7^4 + 9^4 + 9^4 = 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 9^4 + 9^4.
%o A345829 (Python)
%o A345829 from itertools import combinations_with_replacement as cwr
%o A345829 from collections import defaultdict
%o A345829 keep = defaultdict(lambda: 0)
%o A345829 power_terms = [x**4 for x in range(1, 1000)]
%o A345829 for pos in cwr(power_terms, 7):
%o A345829     tot = sum(pos)
%o A345829     keep[tot] += 1
%o A345829     rets = sorted([k for k, v in keep.items() if v == 7])
%o A345829     for x in range(len(rets)):
%o A345829         print(rets[x])
%Y A345829 Cf. A345573, A345779, A345819, A345828, A345830, A345839, A346284.
%K A345829 nonn
%O A345829 1,1
%A A345829 _David Consiglio, Jr._, Jun 26 2021