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Numbers that are the sum of six squares in one or more ways.
4

%I #20 May 10 2024 01:38:27

%S 6,9,12,14,15,17,18,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,

%T 36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,

%U 59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77

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

%H Sean A. Irvine, <a href="/A344805/b344805.txt">Table of n, a(n) for n = 1..1000</a>

%e 9 is a term because 9 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2.

%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 >= 1])

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

%o print(rets[x])

%Y Cf. A003329, A047700, A344806, A345478.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 19 2021