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A344807 Numbers that are the sum of six squares in three or more ways.

%I A344807 #11 May 10 2024 01:37:35
%S A344807 30,33,36,38,39,41,44,45,46,47,48,49,50,51,52,53,54,55,56,57,59,60,61,
%T A344807 62,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,
%U A344807 86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103
%N A344807 Numbers that are the sum of six squares in three or more ways.
%H A344807 Sean A. Irvine, <a href="/A344807/b344807.txt">Table of n, a(n) for n = 1..1000</a>
%e A344807 33 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 5^2
%e A344807    = 1^2 + 1^2 + 2^2 + 3^2 + 3^2 + 3^2
%e A344807    = 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2
%e A344807 so 33 is a term.
%o A344807 (Python)
%o A344807 from itertools import combinations_with_replacement as cwr
%o A344807 from collections import defaultdict
%o A344807 keep = defaultdict(lambda: 0)
%o A344807 power_terms = [x**2 for x in range(1, 1000)]
%o A344807 for pos in cwr(power_terms, 6):
%o A344807     tot = sum(pos)
%o A344807     keep[tot] += 1
%o A344807     rets = sorted([k for k, v in keep.items() if v >= 3])
%o A344807     for x in range(len(rets)):
%o A344807         print(rets[x])
%Y A344807 Cf. A344796, A344806, A344808, A345480, A345512.
%K A344807 nonn
%O A344807 1,1
%A A344807 _David Consiglio, Jr._, Jun 20 2021