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A345481 Numbers that are the sum of seven squares in four or more ways.

%I A345481 #10 May 10 2024 01:37:45
%S A345481 37,40,42,45,46,48,49,50,52,53,54,55,57,58,60,61,62,63,64,65,66,67,69,
%T A345481 70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,
%U A345481 93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108
%N A345481 Numbers that are the sum of seven squares in four or more ways.
%H A345481 Sean A. Irvine, <a href="/A345481/b345481.txt">Table of n, a(n) for n = 1..1000</a>
%e A345481 40 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 4^2 + 4^2
%e A345481    = 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 5^2
%e A345481    = 1^2 + 2^2 + 2^2 + 2^2 + 3^2 + 3^2 + 3^2
%e A345481    = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2
%e A345481 so 40 is a term.
%o A345481 (Python)
%o A345481 from itertools import combinations_with_replacement as cwr
%o A345481 from collections import defaultdict
%o A345481 keep = defaultdict(lambda: 0)
%o A345481 power_terms = [x**2 for x in range(1, 1000)]
%o A345481 for pos in cwr(power_terms, 7):
%o A345481     tot = sum(pos)
%o A345481     keep[tot] += 1
%o A345481     rets = sorted([k for k, v in keep.items() if v >= 4])
%o A345481     for x in range(len(rets)):
%o A345481         print(rets[x])
%Y A345481 Cf. A344808, A345480, A345482, A345491, A345522.
%K A345481 nonn
%O A345481 1,1
%A A345481 _David Consiglio, Jr._, Jun 20 2021