cp's OEIS Frontend

A345495 Numbers that are the sum of eight squares in eight or more ways.

%I A345495 #6 Aug 05 2021 07:20:05
%S A345495 56,59,62,64,65,67,68,70,71,73,74,75,76,77,78,79,80,81,82,83,84,85,86,
%T A345495 87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,
%U A345495 107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122
%N A345495 Numbers that are the sum of eight squares in eight or more ways.
%H A345495 Sean A. Irvine, <a href="/A345495/b345495.txt">Table of n, a(n) for n = 1..1000</a>
%e A345495 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 A345495 (Python)
%o A345495 from itertools import combinations_with_replacement as cwr
%o A345495 from collections import defaultdict
%o A345495 keep = defaultdict(lambda: 0)
%o A345495 power_terms = [x**2 for x in range(1, 1000)]
%o A345495 for pos in cwr(power_terms, 8):
%o A345495     tot = sum(pos)
%o A345495     keep[tot] += 1
%o A345495     rets = sorted([k for k, v in keep.items() if v >= 8])
%o A345495     for x in range(len(rets)):
%o A345495         print(rets[x])
%Y A345495 Cf. A345485, A345494, A345496, A345505, A345538.
%K A345495 nonn
%O A345495 1,1
%A A345495 _David Consiglio, Jr._, Jun 20 2021