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A344808 Numbers that are the sum of six squares in four or more ways.

%I A344808 #11 May 10 2024 01:38:08
%S A344808 36,41,44,45,53,54,56,57,60,62,63,65,66,68,69,70,71,72,73,74,75,76,77,
%T A344808 78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,
%U A344808 100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115
%N A344808 Numbers that are the sum of six squares in four or more ways.
%H A344808 Sean A. Irvine, <a href="/A344808/b344808.txt">Table of n, a(n) for n = 1..1000</a>
%e A344808 41 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 6^2
%e A344808    = 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 5^2
%e A344808    = 1^2 + 2^2 + 3^2 + 3^2 + 3^2 + 3^2
%e A344808    = 2^2 + 2^2 + 2^2 + 2^2 + 3^2 + 4^2
%e A344808 so 41 is a term.
%o A344808 (Python)
%o A344808 from itertools import combinations_with_replacement as cwr
%o A344808 from collections import defaultdict
%o A344808 keep = defaultdict(lambda: 0)
%o A344808 power_terms = [x**2 for x in range(1, 1000)]
%o A344808 for pos in cwr(power_terms, 6):
%o A344808     tot = sum(pos)
%o A344808     keep[tot] += 1
%o A344808     rets = sorted([k for k, v in keep.items() if v >= 4])
%o A344808     for x in range(len(rets)):
%o A344808         print(rets[x])
%Y A344808 Cf. A344797, A344807, A344809, A345481, A345513.
%K A344808 nonn
%O A344808 1,1
%A A344808 _David Consiglio, Jr._, Jun 20 2021