cp's OEIS Frontend

A345576 Numbers that are the sum of seven fourth powers in ten or more ways.

%I A345576 #6 Jul 31 2021 17:58:20
%S A345576 31251,44547,45827,45892,45907,47667,47971,48292,49572,49812,50052,
%T A345576 51092,52372,53316,53476,54531,54596,54756,54996,57411,58036,58116,
%U A345576 58276,58516,58660,58756,59331,59781,59796,59811,59827,59861,59876,59892,60036,60371,60436
%N A345576 Numbers that are the sum of seven fourth powers in ten or more ways.
%H A345576 Sean A. Irvine, <a href="/A345576/b345576.txt">Table of n, a(n) for n = 1..10000</a>
%e A345576 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 A345576 (Python)
%o A345576 from itertools import combinations_with_replacement as cwr
%o A345576 from collections import defaultdict
%o A345576 keep = defaultdict(lambda: 0)
%o A345576 power_terms = [x**4 for x in range(1, 1000)]
%o A345576 for pos in cwr(power_terms, 7):
%o A345576     tot = sum(pos)
%o A345576     keep[tot] += 1
%o A345576     rets = sorted([k for k, v in keep.items() if v >= 10])
%o A345576     for x in range(len(rets)):
%o A345576         print(rets[x])
%Y A345576 Cf. A345506, A345567, A345575, A345585, A345643, A345832.
%K A345576 nonn
%O A345576 1,1
%A A345576 _David Consiglio, Jr._, Jun 20 2021