A344751 - OEIS

%I #10 Jul 31 2021 22:17:32

%S 105760443698,131801075042,187758243218,253590205778,319889609522,

%T 445600096578,510334859762,601395185762,615665999858,730871934338,

%U 749472385298,855952663202,856722174098,951843993282,1157106866258,1186209675378,1290443616098,1455023522498

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

%C Differs from A344750 at term 1 because 49511121842 = 13^4 + 390^4 + 403^4  = 35^4 + 378^4 + 413^4  = 70^4 + 357^4 + 427^4  = 103^4 + 335^4 + 438^4  = 117^4 + 325^4 + 442^4  = 137^4 + 310^4 + 447^4  = 175^4 + 322^4 + 441^4  = 182^4 + 273^4 + 455^4  = 202^4 + 255^4 + 457^4  = 225^4 + 233^4 + 458^4.

%H David Consiglio, Jr., <a href="/A344751/b344751.txt">Table of n, a(n) for n = 1..23</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. A344738, A344750, A344861, A344927, A345120.

%K nonn

%O 1,1

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