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%I A345480 #6 Aug 05 2021 07:21:22
%S A345480 31,34,37,39,40,42,43,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,
%T A345480 61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,
%U A345480 84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101
%N A345480 Numbers that are the sum of seven squares in three or more ways.
%H A345480 Sean A. Irvine, <a href="/A345480/b345480.txt">Table of n, a(n) for n = 1..1000</a>
%e A345480 34 is a term because 34 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 5^2 = 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 3^2 + 3^2 = 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2.
%o A345480 (Python)
%o A345480 from itertools import combinations_with_replacement as cwr
%o A345480 from collections import defaultdict
%o A345480 keep = defaultdict(lambda: 0)
%o A345480 power_terms = [x**2 for x in range(1, 1000)]
%o A345480 for pos in cwr(power_terms, 7):
%o A345480     tot = sum(pos)
%o A345480     keep[tot] += 1
%o A345480     rets = sorted([k for k, v in keep.items() if v >= 3])
%o A345480     for x in range(len(rets)):
%o A345480         print(rets[x])
%Y A345480 Cf. A344807, A345479, A345481, A345490, A345521.
%K A345480 nonn
%O A345480 1,1
%A A345480 _David Consiglio, Jr._, Jun 20 2021

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