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A344353 Numbers that are the sum of four fourth powers in exactly four ways.

%I A344353 #13 Jul 31 2021 22:12:05
%S A344353 236674,282018,300834,334818,478338,637794,650034,650658,708483,
%T A344353 708834,729938,789378,816578,832274,849954,941859,989043,1042083,
%U A344353 1045539,1099203,1099458,1102258,1179378,1243074,1257954,1283874,1323234,1334979,1339074,1342979,1352898,1357059,1379043,1518578
%N A344353 Numbers that are the sum of four fourth powers in exactly four ways.
%C A344353 Differs from A344352 at term 52 because 2147874 = 2^4 + 14^4 + 31^4 + 33^4 = 4^4 + 23^4 + 27^4 + 34^4 = 7^4 + 21^4 + 28^4 + 34^4 = 12^4 + 17^4 + 29^4 + 34^4 = 14^4 + 18^4 + 19^4 + 37^4.
%H A344353 David Consiglio, Jr., <a href="/A344353/b344353.txt">Table of n, a(n) for n = 1..20000</a>
%e A344353 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 A344353 (Python)
%o A344353 from itertools import combinations_with_replacement as cwr
%o A344353 from collections import defaultdict
%o A344353 keep = defaultdict(lambda: 0)
%o A344353 power_terms = [x**4 for x in range(1,200)]
%o A344353 count = 1
%o A344353 for pos in cwr(power_terms,4):
%o A344353     tot = sum(pos)
%o A344353     keep[tot] += 1
%o A344353     count += 1
%o A344353 rets = sorted([k for k,v in keep.items() if v == 4])
%o A344353 for x in range(len(rets)):
%o A344353     print(rets[x])
%Y A344353 Cf. A343972, A344242, A344278, A344352, A344355, A344357.
%K A344353 nonn
%O A344353 1,1
%A A344353 _David Consiglio, Jr._, May 15 2021