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A344809 Numbers that are the sum of six squares in five or more ways. 6

%I

%S 54,57,60,62,63,65,66,68,69,70,71,72,73,74,75,76,77,78,79,80,81,83,84,

%T 85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,

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

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

%H Sean A. Irvine, <a href="/A344809/b344809.txt">Table of n, a(n) for n = 1..1000</a>

%e 57 is a term because 57 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 7^2 = 1^2 + 1^2 + 1^2 + 2^2 + 5^2 + 5^2 = 1^2 + 1^2 + 1^2 + 3^2 + 3^2 + 6^2 = 1^2 + 2^2 + 2^2 + 4^2 + 4^2 + 4^2 = 1^2 + 2^2 + 3^2 + 3^2 + 3^2 + 5^2 = 2^2 + 2^2 + 2^2 + 2^2 + 4^2 + 5^2.

%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, 6):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v >= 5])

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

%o print(rets[x])

%Y Cf. A344798, A344808, A344810, A345482, A345514.

%K nonn

%O 1,1

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

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Last modified January 16 23:11 EST 2022. Contains 350377 sequences. (Running on oeis4.)