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A345634 Numbers that are the sum of ten fifth powers in two or more ways.

%I A345634 #7 Jul 31 2021 15:58:12
%S A345634 4102,4133,4164,4195,4226,4257,4344,4375,4406,4437,4468,4586,4617,
%T A345634 4648,4679,4828,4859,4890,5070,5101,5125,5156,5187,5218,5249,5312,
%U A345634 5367,5398,5429,5460,5609,5640,5671,5851,5882,6093,6148,6179,6210,6241,6390,6421,6452
%N A345634 Numbers that are the sum of ten fifth powers in two or more ways.
%H A345634 Sean A. Irvine, <a href="/A345634/b345634.txt">Table of n, a(n) for n = 1..10000</a>
%e A345634 4133 is a term because 4133 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 4^5 + 4^5 + 4^5 + 4^5 = 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5.
%o A345634 (Python)
%o A345634 from itertools import combinations_with_replacement as cwr
%o A345634 from collections import defaultdict
%o A345634 keep = defaultdict(lambda: 0)
%o A345634 power_terms = [x**5 for x in range(1, 1000)]
%o A345634 for pos in cwr(power_terms, 10):
%o A345634     tot = sum(pos)
%o A345634     keep[tot] += 1
%o A345634     rets = sorted([k for k, v in keep.items() if v >= 2])
%o A345634     for x in range(len(rets)):
%o A345634         print(rets[x])
%Y A345634 Cf. A003355, A345595, A345619, A345635, A346347.
%K A345634 nonn
%O A345634 1,1
%A A345634 _David Consiglio, Jr._, Jun 20 2021