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A345502 Numbers that are the sum of nine squares in five or more ways.

%I A345502 #6 Aug 05 2021 07:18:15
%S A345502 47,48,50,51,53,54,55,56,57,58,59,60,62,63,64,65,66,67,68,69,70,71,72,
%T A345502 73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,
%U A345502 96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111
%N A345502 Numbers that are the sum of nine squares in five or more ways.
%H A345502 Sean A. Irvine, <a href="/A345502/b345502.txt">Table of n, a(n) for n = 1..1000</a>
%e A345502 48 is a term because 48 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 4^2 + 5^2 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 3^2 + 3^2 + 3^2 + 4^2 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 4^2 + 4^2 = 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 5^2 = 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 3^2 + 3^2 + 3^2 = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2.
%o A345502 (Python)
%o A345502 from itertools import combinations_with_replacement as cwr
%o A345502 from collections import defaultdict
%o A345502 keep = defaultdict(lambda: 0)
%o A345502 power_terms = [x**2 for x in range(1, 1000)]
%o A345502 for pos in cwr(power_terms, 9):
%o A345502     tot = sum(pos)
%o A345502     keep[tot] += 1
%o A345502     rets = sorted([k for k, v in keep.items() if v >= 5])
%o A345502     for x in range(len(rets)):
%o A345502         print(rets[x])
%Y A345502 Cf. A345492, A345501, A345503, A345544, A346804.
%K A345502 nonn
%O A345502 1,1
%A A345502 _David Consiglio, Jr._, Jun 20 2021