cp's OEIS Frontend

A345826 Numbers that are the sum of seven fourth powers in exactly four ways.

%I A345826 #6 Jul 31 2021 21:36:46
%S A345826 2932,4147,4212,4387,5427,5602,5667,6627,6692,6817,6822,6837,6852,
%T A345826 6867,7012,7122,7251,7316,7491,7747,7857,8052,8097,8162,8402,8467,
%U A345826 8532,8707,8787,9027,9092,9157,9172,9202,9237,9252,9332,9412,9442,9492,9572,9652,9682
%N A345826 Numbers that are the sum of seven fourth powers in exactly four ways.
%C A345826 Differs from A345570 at term 9 because 6642 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 9^4  = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 7^4 + 8^4  = 2^4 + 2^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4  = 2^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4  = 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4.
%H A345826 Sean A. Irvine, <a href="/A345826/b345826.txt">Table of n, a(n) for n = 1..10000</a>
%e A345826 4147 is a term because 4147 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 8^4 = 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 + 6^4 = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4.
%o A345826 (Python)
%o A345826 from itertools import combinations_with_replacement as cwr
%o A345826 from collections import defaultdict
%o A345826 keep = defaultdict(lambda: 0)
%o A345826 power_terms = [x**4 for x in range(1, 1000)]
%o A345826 for pos in cwr(power_terms, 7):
%o A345826     tot = sum(pos)
%o A345826     keep[tot] += 1
%o A345826     rets = sorted([k for k, v in keep.items() if v == 4])
%o A345826     for x in range(len(rets)):
%o A345826         print(rets[x])
%Y A345826 Cf. A345570, A345776, A345816, A345825, A345827, A345836, A346281.
%K A345826 nonn
%O A345826 1,1
%A A345826 _David Consiglio, Jr._, Jun 26 2021