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A344648 Numbers that are the sum of three fourth powers in exactly six ways.

%I A344648 #11 Jan 04 2022 10:31:13
%S A344648 292965218,1010431058,1110995522,1500533762,1665914642,2158376402,
%T A344648 2373191618,2636686962,2689817858,3019732898,3205282178,3642994082,
%U A344648 3831800882,4324686002,4687443488,5064808658,5175310322,6317554418,6450435362,6720346178,7018992162,7635761042,7781780258
%N A344648 Numbers that are the sum of three fourth powers in exactly six ways.
%C A344648 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 A344648 Sean A. Irvine, <a href="/A344648/b344648.txt">Table of n, a(n) for n = 1..5000</a>
%e A344648 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 A344648 (Python)
%o A344648 from itertools import combinations_with_replacement as cwr
%o A344648 from collections import defaultdict
%o A344648 keep = defaultdict(lambda: 0)
%o A344648 power_terms = [x**4 for x in range(1, 500)]
%o A344648 for pos in cwr(power_terms, 3):
%o A344648     tot = sum(pos)
%o A344648     keep[tot] += 1
%o A344648 rets = sorted([k for k, v in keep.items() if v == 6])
%o A344648 for x in range(len(rets)):
%o A344648     print(rets[x])
%Y A344648 Cf. A344365, A344647, A344730, A344921, A345084.
%K A344648 nonn
%O A344648 1,1
%A A344648 _David Consiglio, Jr._, May 25 2021