login
Numbers that are the sum of seven squares in four or more ways.
6

%I #10 May 10 2024 01:37:45

%S 37,40,42,45,46,48,49,50,52,53,54,55,57,58,60,61,62,63,64,65,66,67,69,

%T 70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,

%U 93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108

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

%H Sean A. Irvine, <a href="/A345481/b345481.txt">Table of n, a(n) for n = 1..1000</a>

%e 40 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 4^2 + 4^2

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

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

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

%e so 40 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, 7):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v >= 4])

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

%o print(rets[x])

%Y Cf. A344808, A345480, A345482, A345491, A345522.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 20 2021