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A344806 Numbers that are the sum of six squares in two or more ways.

%I A344806 #11 May 10 2024 01:37:57
%S A344806 21,24,29,30,33,36,38,39,41,42,44,45,46,47,48,49,50,51,52,53,54,55,56,
%T A344806 57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,
%U A344806 80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98
%N A344806 Numbers that are the sum of six squares in two or more ways.
%H A344806 Sean A. Irvine, <a href="/A344806/b344806.txt">Table of n, a(n) for n = 1..1000</a>
%e A344806 24 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 4^2
%e A344806    = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2
%e A344806 so 24 is a term.
%o A344806 (Python)
%o A344806 from itertools import combinations_with_replacement as cwr
%o A344806 from collections import defaultdict
%o A344806 keep = defaultdict(lambda: 0)
%o A344806 power_terms = [x**2 for x in range(1, 1000)]
%o A344806 for pos in cwr(power_terms, 6):
%o A344806     tot = sum(pos)
%o A344806     keep[tot] += 1
%o A344806     rets = sorted([k for k, v in keep.items() if v >= 2])
%o A344806     for x in range(len(rets)):
%o A344806         print(rets[x])
%Y A344806 Cf. A344795, A344805, A344807, A345479, A345511.
%K A344806 nonn
%O A344806 1,1
%A A344806 _David Consiglio, Jr._, Jun 20 2021