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A345494 Numbers that are the sum of eight squares in seven or more ways.

%I A345494 #6 Aug 05 2021 07:20:01
%S A345494 56,59,62,64,65,67,68,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,
%T A345494 86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,
%U A345494 106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121
%N A345494 Numbers that are the sum of eight squares in seven or more ways.
%H A345494 Sean A. Irvine, <a href="/A345494/b345494.txt">Table of n, a(n) for n = 1..1000</a>
%e A345494 59 is a term because 59 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 7^2 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 5^2 + 5^2 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 3^2 + 3^2 + 6^2 = 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 4^2 + 4^2 + 4^2 = 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 3^2 + 3^2 + 5^2 = 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2 + 5^2 = 1^2 + 2^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 = 2^2 + 2^2 + 2^2 + 2^2 + 3^2 + 3^2 + 3^2 + 4^2.
%o A345494 (Python)
%o A345494 from itertools import combinations_with_replacement as cwr
%o A345494 from collections import defaultdict
%o A345494 keep = defaultdict(lambda: 0)
%o A345494 power_terms = [x**2 for x in range(1, 1000)]
%o A345494 for pos in cwr(power_terms, 8):
%o A345494     tot = sum(pos)
%o A345494     keep[tot] += 1
%o A345494     rets = sorted([k for k, v in keep.items() if v >= 7])
%o A345494     for x in range(len(rets)):
%o A345494         print(rets[x])
%Y A345494 Cf. A345484, A345493, A345495, A345504, A345537.
%K A345494 nonn
%O A345494 1,1
%A A345494 _David Consiglio, Jr._, Jun 20 2021