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A345491 Numbers that are the sum of eight squares in four or more ways.

%I A345491 #6 Aug 05 2021 07:19:51
%S A345491 32,38,41,43,44,46,47,49,50,51,52,53,54,55,56,57,58,59,61,62,63,64,65,
%T A345491 66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,
%U A345491 89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105
%N A345491 Numbers that are the sum of eight squares in four or more ways.
%H A345491 Sean A. Irvine, <a href="/A345491/b345491.txt">Table of n, a(n) for n = 1..1000</a>
%e A345491 38 is a term because 38 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 4^2 + 4^2 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 5^2 = 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 3^2 + 3^2 + 3^2 = 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2.
%o A345491 (Python)
%o A345491 from itertools import combinations_with_replacement as cwr
%o A345491 from collections import defaultdict
%o A345491 keep = defaultdict(lambda: 0)
%o A345491 power_terms = [x**2 for x in range(1, 1000)]
%o A345491 for pos in cwr(power_terms, 8):
%o A345491     tot = sum(pos)
%o A345491     keep[tot] += 1
%o A345491     rets = sorted([k for k, v in keep.items() if v >= 4])
%o A345491     for x in range(len(rets)):
%o A345491         print(rets[x])
%Y A345491 Cf. A345481, A345490, A345492, A345501, A345534.
%K A345491 nonn
%O A345491 1,1
%A A345491 _David Consiglio, Jr._, Jun 20 2021