%I #10 May 10 2024 02:17:58

%S 61,64,66,67,69,70,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,

%T 89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,

%U 109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124

%N Numbers that are the sum of ten squares in ten or more ways.

%H Sean A. Irvine, <a href="/A346808/b346808.txt">Table of n, a(n) for n = 1..10000</a>

%e 64 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 7^2

%e = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 3^2 + 6^2

%e = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 5^2 + 5^2

%e = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 4^2 + 4^2 + 5^2

%e = 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2 + 5^2

%e = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 3^2 + 3^2 + 3^2 + 5^2

%e = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 4^2 + 4^2 + 4^2

%e = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 3^2 + 3^2 + 3^2 + 4^2 + 4^2

%e = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2 + 4^2

%e = 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 3^2 + 3^2 + 3^2 + 4^2

%e = 1^2 + 1^2 + 2^2 + 2^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2

%e so 64 is a term.

%o (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**2 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 10):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v >= 10])

%o for x in range(len(rets)):

%o print(rets[x])

%Y Cf. A345558, A346803. Subsequence of A346807.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Aug 04 2021