cp's OEIS Frontend

A345832 Numbers that are the sum of seven fourth powers in exactly ten ways.

%I A345832 #6 Jul 31 2021 21:39:39
%S A345832 31251,44547,45827,45892,47667,47971,49572,51092,53316,53476,54531,
%T A345832 54596,54756,57411,58276,58660,59781,59811,59827,59861,59876,59892,
%U A345832 61076,64581,65876,65891,66356,66596,66676,67716,67876,68131,68322,68772,69171,69667,70116
%N A345832 Numbers that are the sum of seven fourth powers in exactly ten ways.
%C A345832 Differs from A345576 at term 5 because 45907 = 1^4 + 1^4 + 3^4 + 4^4 + 8^4 + 12^4 + 12^4  = 1^4 + 6^4 + 6^4 + 8^4 + 8^4 + 9^4 + 13^4  = 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 11^4 + 13^4  = 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 11^4 + 13^4  = 2^4 + 2^4 + 4^4 + 7^4 + 7^4 + 7^4 + 14^4  = 2^4 + 3^4 + 6^4 + 6^4 + 7^4 + 7^4 + 14^4  = 2^4 + 4^4 + 6^4 + 7^4 + 9^4 + 11^4 + 12^4  = 2^4 + 5^4 + 5^4 + 10^4 + 10^4 + 10^4 + 11^4  = 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 9^4 + 14^4  = 3^4 + 6^4 + 6^4 + 6^4 + 9^4 + 11^4 + 12^4  = 4^4 + 7^4 + 7^4 + 8^4 + 8^4 + 8^4 + 13^4.
%H A345832 Sean A. Irvine, <a href="/A345832/b345832.txt">Table of n, a(n) for n = 1..10000</a>
%e A345832 44547 is a term because 44547 = 1^4 + 2^4 + 2^4 + 2^4 + 6^4 + 11^4 + 13^4 = 1^4 + 2^4 + 2^4 + 6^4 + 7^4 + 7^4 + 14^4 = 1^4 + 2^4 + 6^4 + 6^4 + 9^4 + 11^4 + 12^4 = 1^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4 + 13^4 = 2^4 + 2^4 + 8^4 + 9^4 + 9^4 + 9^4 + 12^4 = 2^4 + 4^4 + 6^4 + 6^4 + 9^4 + 9^4 + 13^4 = 2^4 + 4^4 + 7^4 + 7^4 + 8^4 + 11^4 + 12^4 = 3^4 + 3^4 + 4^4 + 4^4 + 7^4 + 12^4 + 12^4 = 3^4 + 6^4 + 6^4 + 7^4 + 8^4 + 11^4 + 12^4 = 4^4 + 4^4 + 8^4 + 8^4 + 9^4 + 11^4 + 11^4.
%o A345832 (Python)
%o A345832 from itertools import combinations_with_replacement as cwr
%o A345832 from collections import defaultdict
%o A345832 keep = defaultdict(lambda: 0)
%o A345832 power_terms = [x**4 for x in range(1, 1000)]
%o A345832 for pos in cwr(power_terms, 7):
%o A345832     tot = sum(pos)
%o A345832     keep[tot] += 1
%o A345832     rets = sorted([k for k, v in keep.items() if v == 10])
%o A345832     for x in range(len(rets)):
%o A345832         print(rets[x])
%Y A345832 Cf. A345576, A345782, A345822, A345831, A345842, A346259.
%K A345832 nonn
%O A345832 1,1
%A A345832 _David Consiglio, Jr._, Jun 26 2021