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A345479 Numbers that are the sum of seven squares in two or more ways.

%I A345479 #10 May 10 2024 01:39:04
%S A345479 22,25,28,30,31,33,34,37,38,39,40,42,43,45,46,47,48,49,50,51,52,53,54,
%T A345479 55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,
%U A345479 78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96
%N A345479 Numbers that are the sum of seven squares in two or more ways.
%H A345479 Sean A. Irvine, <a href="/A345479/b345479.txt">Table of n, a(n) for n = 1..1000</a>
%e A345479 25 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 4^2
%e A345479    = 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2
%e A345479 so 25 is a term.
%o A345479 (Python)
%o A345479 from itertools import combinations_with_replacement as cwr
%o A345479 from collections import defaultdict
%o A345479 keep = defaultdict(lambda: 0)
%o A345479 power_terms = [x**2 for x in range(1, 1000)]
%o A345479 for pos in cwr(power_terms, 7):
%o A345479     tot = sum(pos)
%o A345479     keep[tot] += 1
%o A345479     rets = sorted([k for k, v in keep.items() if v >= 2])
%o A345479     for x in range(len(rets)):
%o A345479         print(rets[x])
%Y A345479 Cf. A344806, A345478, A345480, A345489, A345520.
%K A345479 nonn
%O A345479 1,1
%A A345479 _David Consiglio, Jr._, Jun 20 2021