A344811 - OEIS

%I #11 May 10 2024 01:39:13

%S 60,65,68,69,77,78,81,84,86,87,89,90,92,93,94,95,96,97,98,99,100,101,

%T 102,103,104,105,107,108,109,110,111,112,113,114,115,116,117,118,119,

%U 120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136

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

%H Sean A. Irvine, <a href="/A344811/b344811.txt">Table of n, a(n) for n = 1..1000</a>

%e 65 = 1^2 + 1^2 + 1^2 + 1^2 + 5^2 + 6^2

%e    = 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 7^2

%e    = 1^2 + 1^2 + 2^2 + 3^2 + 5^2 + 5^2

%e    = 1^2 + 1^2 + 3^2 + 3^2 + 3^2 + 6^2

%e    = 1^2 + 2^2 + 2^2 + 2^2 + 4^2 + 6^2

%e    = 2^2 + 2^2 + 3^2 + 4^2 + 4^2 + 4^2

%e    = 2^2 + 3^2 + 3^2 + 3^2 + 3^2 + 5^2

%e so 65 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 >= 7])

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

%o         print(rets[x])

%Y Cf. A344800, A344810, A344812, A345484, A345516.

%K nonn

%O 1,1

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