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A344278 Numbers that are the sum of three fourth powers in exactly four ways.

%I A344278 #8 Jul 31 2021 22:17:16
%S A344278 5978882,15916082,20621042,22673378,30623138,33998258,39765362,
%T A344278 48432482,53809938,61627202,65413922,74346818,84942578,88258898,
%U A344278 95662112,103363442,117259298,128929682,131641538,137149922,143244738,155831858,158811842,167042642,174135122,175706258,188529362
%N A344278 Numbers that are the sum of three fourth powers in exactly four ways.
%C A344278 Differs from A344277 at term 37 because 292965218 = 2^4 + 109^4 + 111^4 = 21^4 + 98^4 + 119^4 = 27^4 + 94^4 + 121^4 = 34^4 + 89^4 + 123^4 = 49^4 + 77^4 + 126^4 = 61^4 + 66^4 + 127^4
%H A344278 David Consiglio, Jr., <a href="/A344278/b344278.txt">Table of n, a(n) for n = 1..7946</a>
%e A344278 20621042 is a member of this sequence because 20621042 = 5^4 + 54^4 + 59^4 = 10^4 + 51^4 + 61^4 = 25^4 + 46^4 + 63^4 = 26^4 + 39^4 + 65^4
%o A344278 (Python)
%o A344278 from itertools import combinations_with_replacement as cwr
%o A344278 from collections import defaultdict
%o A344278 keep = defaultdict(lambda: 0)
%o A344278 power_terms = [x**4 for x in range(1,50)]
%o A344278 for pos in cwr(power_terms,3):
%o A344278     tot = sum(pos)
%o A344278     keep[tot] += 1
%o A344278 rets = sorted([k for k,v in keep.items() if v == 4])
%o A344278 for x in range(len(rets)):
%o A344278     print(rets[x])
%Y A344278 Cf. A343969, A344240, A344277, A344353, A344365.
%K A344278 nonn
%O A344278 1,1
%A A344278 _David Consiglio, Jr._, May 13 2021