A345839 - OEIS

%I #6 Jul 31 2021 21:33:44

%S 8003,8243,9043,9218,9283,9523,10372,10803,10868,10948,11043,11412,

%T 11557,11587,12083,12692,12932,13188,13333,13508,13972,14147,14387,

%U 14883,14933,14948,14963,15013,15028,15093,15173,15268,15317,15332,15397,15412,15413,15492

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

%C Differs from A345582 at term 19 because 13268 = 1^4 + 1^4 + 1^4 + 2^4 + 6^4 + 6^4 + 8^4 + 9^4  = 1^4 + 1^4 + 2^4 + 4^4 + 7^4 + 7^4 + 8^4 + 8^4  = 1^4 + 1^4 + 3^4 + 6^4 + 6^4 + 7^4 + 8^4 + 8^4  = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4 + 9^4  = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 + 9^4  = 2^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 9^4  = 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 + 9^4  = 4^4 + 4^4 + 4^4 + 5^4 + 5^4 + 5^4 + 5^4 + 10^4.

%H Sean A. Irvine, <a href="/A345839/b345839.txt">Table of n, a(n) for n = 1..10000</a>

%e 8243 is a term because 8243 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 8^4 + 8^4 = 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 + 6^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 6^4 + 9^4 = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 7^4 + 8^4 = 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 8^4 = 2^4 + 4^4 + 4^4 + 4^4 + 4^4 + 7^4 + 7^4 + 7^4 = 3^4 + 4^4 + 4^4 + 4^4 + 6^4 + 6^4 + 7^4 + 7^4.

%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, 8):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o     rets = sorted([k for k, v in keep.items() if v == 7])

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

%o         print(rets[x])

%Y Cf. A345582, A345789, A345829, A345838, A345840, A345849, A346332.

%K nonn

%O 1,1

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