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%I #6 Aug 05 2021 07:16:47
%S 25,28,31,33,34,36,37,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,
%T 55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,
%U 78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96
%N Numbers that are the sum of ten squares in two or more ways.
%H Sean A. Irvine, <a href="/A345509/b345509.txt">Table of n, a(n) for n = 1..1000</a>
%e 28 is a term because 28 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 4^2 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2.
%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**2 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. A345499, A345508, A345510, A345550.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 20 2021
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