A344648 - OEIS

%I #11 Jan 04 2022 10:31:13

%S 292965218,1010431058,1110995522,1500533762,1665914642,2158376402,

%T 2373191618,2636686962,2689817858,3019732898,3205282178,3642994082,

%U 3831800882,4324686002,4687443488,5064808658,5175310322,6317554418,6450435362,6720346178,7018992162,7635761042,7781780258

%N Numbers that are the sum of three fourth powers in exactly six ways.

%C Differs from A344647 at term 2 because 779888018 = 3^4 + 139^4 + 142^4 = 9^4 + 38^4 + 167^4 = 14^4 + 133^4 + 147^4 = 43^4 + 114^4 + 157^4 = 47^4 + 111^4 + 158^4 = 63^4 + 98^4 + 161^4 = 73^4 + 89^4 + 162^4.

%H Sean A. Irvine, <a href="/A344648/b344648.txt">Table of n, a(n) for n = 1..5000</a>

%e 1010431058 is a term because 1010431058 = 13^4 + 143^4 + 156^4 = 31^4 + 132^4 + 163^4 = 44^4 + 123^4 + 167^4 = 52^4 + 117^4 + 169^4 = 69^4 + 103^4 + 172^4 = 81^4 + 92^4 + 173^4.

%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, 500)]

%o for pos in cwr(power_terms, 3):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v == 6])

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

%o     print(rets[x])

%Y Cf. A344365, A344647, A344730, A344921, A345084.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, May 25 2021