A345826 - OEIS

%I #6 Jul 31 2021 21:36:46

%S 2932,4147,4212,4387,5427,5602,5667,6627,6692,6817,6822,6837,6852,

%T 6867,7012,7122,7251,7316,7491,7747,7857,8052,8097,8162,8402,8467,

%U 8532,8707,8787,9027,9092,9157,9172,9202,9237,9252,9332,9412,9442,9492,9572,9652,9682

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

%C 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 Sean A. Irvine, <a href="/A345826/b345826.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**4 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 7):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o     rets = sorted([k for k, v in keep.items() if v == 4])

%o     for x in range(len(rets)):

%o         print(rets[x])

%Y Cf. A345570, A345776, A345816, A345825, A345827, A345836, A346281.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 26 2021