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A345489 Numbers that are the sum of eight squares in two or more ways.

%I A345489 #6 Aug 05 2021 07:19:44
%S A345489 23,26,29,31,32,34,35,37,38,39,40,41,42,43,44,46,47,48,49,50,51,52,53,
%T A345489 54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,
%U A345489 77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95
%N A345489 Numbers that are the sum of eight squares in two or more ways.
%H A345489 Sean A. Irvine, <a href="/A345489/b345489.txt">Table of n, a(n) for n = 1..1000</a>
%e A345489 26 is a term because 26 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 4^2 = 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2.
%o A345489 (Python)
%o A345489 from itertools import combinations_with_replacement as cwr
%o A345489 from collections import defaultdict
%o A345489 keep = defaultdict(lambda: 0)
%o A345489 power_terms = [x**2 for x in range(1, 1000)]
%o A345489 for pos in cwr(power_terms, 8):
%o A345489     tot = sum(pos)
%o A345489     keep[tot] += 1
%o A345489     rets = sorted([k for k, v in keep.items() if v >= 2])
%o A345489     for x in range(len(rets)):
%o A345489         print(rets[x])
%Y A345489 Cf. A345479, A345488, A345490, A345499, A345532.
%K A345489 nonn
%O A345489 1,1
%A A345489 _David Consiglio, Jr._, Jun 20 2021