cp's OEIS Frontend

A345603 Numbers that are the sum of ten fourth powers in ten or more ways.

%I A345603 #6 Jul 31 2021 17:26:15
%S A345603 6885,7990,8035,8100,8165,8275,8340,8515,8565,8580,9140,9205,9235,
%T A345603 9285,9300,9315,9380,9445,9495,9510,9540,9555,9620,9670,9685,9750,
%U A345603 9795,9830,9860,9924,9925,9990,10005,10164,10294,10340,10374,10404,10420,10515,10534
%N A345603 Numbers that are the sum of ten fourth powers in ten or more ways.
%H A345603 Sean A. Irvine, <a href="/A345603/b345603.txt">Table of n, a(n) for n = 1..10000</a>
%e A345603 7990 is a term because 7990 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 6^4 + 6^4 + 6^4 + 8^4 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 6^4 + 9^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 6^4 + 7^4 + 8^4 = 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 4^4 + 4^4 + 7^4 + 7^4 + 7^4 = 1^4 + 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4 + 7^4 + 7^4 = 1^4 + 4^4 + 4^4 + 4^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4 + 8^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 7^4 + 7^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 7^4 + 7^4 = 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 9^4 = 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 6^4 + 7^4.
%o A345603 (Python)
%o A345603 from itertools import combinations_with_replacement as cwr
%o A345603 from collections import defaultdict
%o A345603 keep = defaultdict(lambda: 0)
%o A345603 power_terms = [x**4 for x in range(1, 1000)]
%o A345603 for pos in cwr(power_terms, 10):
%o A345603     tot = sum(pos)
%o A345603     keep[tot] += 1
%o A345603     rets = sorted([k for k, v in keep.items() if v >= 10])
%o A345603     for x in range(len(rets)):
%o A345603         print(rets[x])
%Y A345603 Cf. A345558, A345594, A345602, A345642, A345862.
%K A345603 nonn
%O A345603 1,1
%A A345603 _David Consiglio, Jr._, Jun 20 2021