A344352 - OEIS

%I #9 Jul 31 2021 18:21:55

%S 236674,282018,300834,334818,478338,637794,650034,650658,708483,

%T 708834,729938,789378,816578,832274,849954,941859,989043,1042083,

%U 1045539,1099203,1099458,1102258,1179378,1243074,1257954,1283874,1323234,1334979,1339074,1342979,1352898,1357059,1379043,1518578

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

%H David Consiglio, Jr., <a href="/A344352/b344352.txt">Table of n, a(n) for n = 1..20000</a>

%e 300834 is a term of this sequence because 300834 = 1^4 + 4^4 + 12^4 + 23^4 = 1^4 + 16^4 + 18^4 + 19^4 = 3^4 + 6^4 + 18^4 + 21^4 = 7^4 + 14^4 + 16^4 + 21^4.

%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(1,200)]

%o count = 1

%o for pos in cwr(power_terms,4):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o     count += 1

%o rets = sorted([k for k,v in keep.items() if v >= 4])

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

%o     print(rets[x])

%Y Cf. A343971, A344241, A344277, A344353, A344354, A344356.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, May 15 2021