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Numbers that are the sum of ten fifth powers in two or more ways.
6

%I #7 Jul 31 2021 15:58:12

%S 4102,4133,4164,4195,4226,4257,4344,4375,4406,4437,4468,4586,4617,

%T 4648,4679,4828,4859,4890,5070,5101,5125,5156,5187,5218,5249,5312,

%U 5367,5398,5429,5460,5609,5640,5671,5851,5882,6093,6148,6179,6210,6241,6390,6421,6452

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

%H Sean A. Irvine, <a href="/A345634/b345634.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**5 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 10):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v >= 2])

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

%o print(rets[x])

%Y Cf. A003355, A345595, A345619, A345635, A346347.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 20 2021