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A344861 Numbers that are the sum of three fourth powers in exactly ten ways.

%I A344861 #13 Jul 31 2021 22:17:36
%S A344861 49511121842,364765611938,703409488418,792177949472,2667500248322,
%T A344861 3602781562562,3999861055442,4010400869202,5698033074818,
%U A344861 5836249791008,6330685395762,7250378688098,7695882509378,8746828790882,10383571090802,11254551814688,12160605587858
%N A344861 Numbers that are the sum of three fourth powers in exactly ten ways.
%C A344861 Differs from A344862 at term 2 because 281539574498 = 7^4 + 609^4 + 616^4  = 41^4 + 591^4 + 632^4  = 81^4 + 568^4 + 649^4  = 99^4 + 557^4 + 656^4  = 121^4 + 543^4 + 664^4  = 168^4 + 511^4 + 679^4  = 224^4 + 469^4 + 693^4  = 239^4 + 457^4 + 696^4  = 256^4 + 443^4 + 699^4  = 269^4 + 432^4 + 701^4  = 293^4 + 411^4 + 704^4  = 336^4 + 371^4 + 707^4.
%H A344861 Sean A. Irvine, <a href="/A344861/b344861.txt">Table of n, a(n) for n = 1..40</a>
%e A344861 49511121842 is a term 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.
%o A344861 (Python)
%o A344861 from itertools import combinations_with_replacement as cwr
%o A344861 from collections import defaultdict
%o A344861 keep = defaultdict(lambda: 0)
%o A344861 power_terms = [x**4 for x in range(1, 1000)]
%o A344861 for pos in cwr(power_terms, 3):
%o A344861     tot = sum(pos)
%o A344861     keep[tot] += 1
%o A344861 rets = sorted([k for k, v in keep.items() if v == 10])
%o A344861 for x in range(len(rets)):
%o A344861     print(rets[x])
%Y A344861 Cf. A344751, A344862, A344929, A345122.
%K A344861 nonn
%O A344861 1,1
%A A344861 _David Consiglio, Jr._, May 31 2021
%E A344861 More terms from _Sean A. Irvine_, Jun 01 2021