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Numbers that are the sum of three fourth powers in nine or more ways.
6

%I #10 Jul 31 2021 18:29:26

%S 49511121842,105760443698,131801075042,187758243218,253590205778,

%T 281539574498,319889609522,364765611938,401069383442,445600096578,

%U 510334859762,541692688082,601395185762,615665999858,703409488418,730871934338,749472385298,792177949472

%N Numbers that are the sum of three fourth powers in nine or more ways.

%H David Consiglio, Jr., <a href="/A344750/b344750.txt">Table of n, a(n) for n = 1..41</a>

%e 105760443698 is a term because 105760443698 = 7^4 + 476^4 + 483^4 = 51^4 + 452^4 + 503^4 = 76^4 + 437^4 + 513^4 = 107^4 + 417^4 + 524^4 = 133^4 + 399^4 + 532^4 = 199^4 + 348^4 + 547^4 = 212^4 + 337^4 + 549^4 = 228^4 + 323^4 + 551^4 = 252^4 + 301^4 + 553^4.

%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, 1000)]

%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 >= 9])

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

%o print(rets[x])

%Y Cf. A344737, A344751, A344862, A344926, A345119.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, May 28 2021