A345595 - OEIS

%I #6 Jul 31 2021 17:25:37

%S 265,280,295,310,325,340,345,355,360,375,390,405,420,425,440,455,470,

%T 485,505,520,535,550,565,580,585,595,600,615,630,645,660,665,680,695,

%U 710,725,745,760,775,790,805,820,835,840,855,870,885,889,900,904,919,920

%N Numbers that are the sum of ten fourth powers in two or more ways.

%H Sean A. Irvine, <a href="/A345595/b345595.txt">Table of n, a(n) for n = 1..10000</a>

%e 280 is a term because 280 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4.

%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**4 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 >= 2])

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

%o         print(rets[x])

%Y Cf. A003344, A345550, A345586, A345596, A345634, A345854.

%K nonn

%O 1,1

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