login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

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

%I #11 May 10 2024 01:37:57

%S 21,24,29,30,33,36,38,39,41,42,44,45,46,47,48,49,50,51,52,53,54,55,56,

%T 57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,

%U 80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98

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

%H Sean A. Irvine, <a href="/A344806/b344806.txt">Table of n, a(n) for n = 1..1000</a>

%e 24 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 4^2

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

%e so 24 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, 6):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v >= 2])

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

%o print(rets[x])

%Y Cf. A344795, A344805, A344807, A345479, A345511.

%K nonn

%O 1,1

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