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 A346806 Numbers that are the sum of ten squares in seven or more ways. 5

%I #5 Aug 05 2021 07:15:27

%S 57,58,60,61,63,64,66,67,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,

%T 84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,

%U 105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120

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

%H Sean A. Irvine, <a href="/A346806/b346806.txt">Table of n, a(n) for n = 1..10000</a>

%e 58 is a term because 58 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 7^2 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 5^2 + 5^2 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 4^2 + 5^2 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 3^2 + 3^2 + 3^2 + 5^2 = 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 5^2 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 4^2 + 4^2 + 4^2 = 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2 + 4^2 = 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 3^2 + 3^2 + 3^2 + 4^2 = 1^2 + 1^2 + 1^2 + 1^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3.

%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 >= 7])

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

%o print(rets[x])

%Y Cf. A345504, A345555, A346805, A346807.

%K nonn

%O 1,1

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

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Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)