A345829 - OEIS

%I #6 Jul 31 2021 21:36:57

%S 16691,17347,17971,20706,21956,22547,22612,23156,23587,23827,23892,

%T 24436,25107,25427,25716,25971,26051,27812,29092,29187,29332,29427,

%U 29442,29636,29701,29716,29956,29971,30036,30132,30612,30981,30996,31011,31316,31331,31347

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

%C 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 Sean A. Irvine, <a href="/A345829/b345829.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 (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 == 7])

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

%o         print(rets[x])

%Y Cf. A345573, A345779, A345819, A345828, A345830, A345839, A346284.

%K nonn

%O 1,1

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