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A346804 Numbers that are the sum of ten squares in five or more ways.

%I A346804 #9 May 10 2024 02:28:13
%S A346804 40,45,48,49,51,52,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
%T A346804 71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,
%U A346804 94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109
%N A346804 Numbers that are the sum of ten squares in five or more ways.
%H A346804 Sean A. Irvine, <a href="/A346804/b346804.txt">Table of n, a(n) for n = 1..10000</a>
%e A346804 45 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 6^2
%e A346804    = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 5^2
%e A346804    = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 3^2 + 4^2
%e A346804    = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 3^2 + 3^2 + 3^2
%e A346804    = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 3^2
%e A346804 so 45 is a term.
%o A346804 (Python)
%o A346804 from itertools import combinations_with_replacement as cwr
%o A346804 from collections import defaultdict
%o A346804 keep = defaultdict(lambda: 0)
%o A346804 power_terms = [x**2 for x in range(1, 1000)]
%o A346804 for pos in cwr(power_terms, 10):
%o A346804     tot = sum(pos)
%o A346804     keep[tot] += 1
%o A346804     rets = sorted([k for k, v in keep.items() if v >= 5])
%o A346804     for x in range(len(rets)):
%o A346804         print(rets[x])
%Y A346804 Cf. A345502, A345553, A346805.
%K A346804 nonn
%O A346804 1,1
%A A346804 _David Consiglio, Jr._, Aug 04 2021