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A346805 Numbers that are the sum of ten squares in six or more ways.

%I A346805 #11 May 10 2024 02:28:01
%S A346805 49,52,55,57,58,60,61,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,
%T A346805 79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,
%U A346805 101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116
%N A346805 Numbers that are the sum of ten squares in six or more ways.
%H A346805 Sean A. Irvine, <a href="/A346805/b346805.txt">Table of n, a(n) for n = 1..10000</a>
%e A346805 52 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 4^2 + 5^2
%e A346805    = 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 5^2
%e A346805    = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2 + 4^2
%e A346805    = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 3^2 + 3^2 + 4^2
%e A346805    = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2
%e A346805    = 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 3^2 + 3^2 + 3^2
%e A346805 so 52 is a term.
%t A346805 Select[Range[120],Count[IntegerPartitions[#,{10}],_?(AllTrue[Sqrt[#],IntegerQ]&)]>5&] (* _Harvey P. Dale_, Sep 10 2023 *)
%o A346805 (Python)
%o A346805 from itertools import combinations_with_replacement as cwr
%o A346805 from collections import defaultdict
%o A346805 keep = defaultdict(lambda: 0)
%o A346805 power_terms = [x**2 for x in range(1, 1000)]
%o A346805 for pos in cwr(power_terms, 10):
%o A346805     tot = sum(pos)
%o A346805     keep[tot] += 1
%o A346805     rets = sorted([k for k, v in keep.items() if v >= 6])
%o A346805     for x in range(len(rets)):
%o A346805         print(rets[x])
%Y A346805 Cf. A345503, A345554, A346804, A346806.
%K A346805 nonn
%O A346805 1,1
%A A346805 _David Consiglio, Jr._, Aug 04 2021