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A346807 Numbers that are the sum of ten squares in eight or more ways.

%I A346807 #13 May 10 2024 02:26:29
%S A346807 58,61,64,66,67,69,70,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,
%T A346807 88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,
%U A346807 108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123
%N A346807 Numbers that are the sum of ten squares in eight or more ways.
%H A346807 Sean A. Irvine, <a href="/A346807/b346807.txt">Table of n, a(n) for n = 1..10000</a>
%F A346807 a(n) = n + 64 for n >= 8 (conjectured). - _Chai Wah Wu_, Dec 05 2023
%e A346807 61 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 7^2
%e A346807    = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 3^2 + 3^2 + 6^2
%e A346807    = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 5^2 + 5^2
%e A346807    = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2 + 5^2
%e A346807    = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 3^2 + 3^2 + 5^2
%e A346807    = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 5^2
%e A346807    = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 4^2 + 4^2 + 4^2
%e A346807    = 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2 + 4^2
%e A346807    = 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 3^2 + 3^2 + 3^2 + 4^2
%e A346807    = 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2
%e A346807 so 61 is a term.
%o A346807 (Python)
%o A346807 from itertools import combinations_with_replacement as cwr
%o A346807 from collections import defaultdict
%o A346807 keep = defaultdict(lambda: 0)
%o A346807 power_terms = [x**2 for x in range(1, 1000)]
%o A346807 for pos in cwr(power_terms, 10):
%o A346807     tot = sum(pos)
%o A346807     keep[tot] += 1
%o A346807     rets = sorted([k for k, v in keep.items() if v >= 8])
%o A346807     for x in range(len(rets)):
%o A346807         print(rets[x])
%Y A346807 Cf. A025434, A345505, A345556, A346806.
%K A346807 nonn
%O A346807 1,1
%A A346807 _David Consiglio, Jr._, Aug 04 2021