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A345505 Numbers that are the sum of nine squares in eight or more ways.

%I A345505 #6 Aug 05 2021 07:18:25
%S A345505 57,60,63,65,66,68,69,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,
%T A345505 87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,
%U A345505 107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122
%N A345505 Numbers that are the sum of nine squares in eight or more ways.
%H A345505 Sean A. Irvine, <a href="/A345505/b345505.txt">Table of n, a(n) for n = 1..1000</a>
%e A345505 60 is a term because 60 = 1^2 + 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 + 1^2 + 2^2 + 5^2 + 5^2 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 3^2 + 3^2 + 6^2 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 4^2 + 4^2 + 4^2 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 3^2 + 3^2 + 5^2 = 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2 + 5^2 = 1^2 + 1^2 + 2^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 = 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 3^2 + 3^2 + 3^2 + 4^2 = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2 + 4^2.
%o A345505 (Python)
%o A345505 from itertools import combinations_with_replacement as cwr
%o A345505 from collections import defaultdict
%o A345505 keep = defaultdict(lambda: 0)
%o A345505 power_terms = [x**2 for x in range(1, 1000)]
%o A345505 for pos in cwr(power_terms, 9):
%o A345505     tot = sum(pos)
%o A345505     keep[tot] += 1
%o A345505     rets = sorted([k for k, v in keep.items() if v >= 8])
%o A345505     for x in range(len(rets)):
%o A345505         print(rets[x])
%Y A345505 Cf. A345495, A345504, A345547, A346807.
%K A345505 nonn
%O A345505 1,1
%A A345505 _David Consiglio, Jr._, Jun 20 2021