%I #8 Jul 31 2021 22:17:16

%S 5978882,15916082,20621042,22673378,30623138,33998258,39765362,

%T 48432482,53809938,61627202,65413922,74346818,84942578,88258898,

%U 95662112,103363442,117259298,128929682,131641538,137149922,143244738,155831858,158811842,167042642,174135122,175706258,188529362

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

%C 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 David Consiglio, Jr., <a href="/A344278/b344278.txt">Table of n, a(n) for n = 1..7946</a>

%e 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 (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(1,50)]

%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 == 4])

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

%o print(rets[x])

%Y Cf. A343969, A344240, A344277, A344353, A344365.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, May 13 2021