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A344357 Numbers that are the sum of four fourth powers in exactly five ways.

%I A344357 #12 Jul 31 2021 22:12:09
%S A344357 2147874,2266338,2690658,3189603,3464178,3754674,4030419,4165794,
%T A344357 4457298,4884114,5229378,5978883,5980178,5981283,6014178,6134994,
%U A344357 6258723,6313953,6400194,6612354,7088898,7498323,7811874,7918498,8064018,8292323,8630259,9146034,9269523,9388978,9397683,9726978
%N A344357 Numbers that are the sum of four fourth powers in exactly five ways.
%C A344357 Differs from A344356 at term 7 because 3847554 = 2^4 + 13^4 + 29^4 + 42^4 = 2^4 + 21^4 + 22^4 + 43^4 = 6^4 + 11^4 + 17^4 + 44^4 = 6^4 + 31^4 + 32^4 + 37^4 = 9^4 + 29^4 + 32^4 + 38^4 = 13^4 + 26^4 + 32^4 + 39^4.
%H A344357 David Consiglio, Jr., <a href="/A344357/b344357.txt">Table of n, a(n) for n = 1..20000</a>
%e A344357 2690658 is a term of this sequence because 2690658 = 2^4 + 8^4 + 33^4 + 35^4 = 3^4 + 4^4 + 19^4 + 40^4 = 7^4 + 8^4 + 30^4 + 37^4 = 9^4 + 21^4 + 30^4 + 36^4 = 16^4 + 25^4 + 32^4 + 33^4.
%o A344357 (Python)
%o A344357 from itertools import combinations_with_replacement as cwr
%o A344357 from collections import defaultdict
%o A344357 keep = defaultdict(lambda: 0)
%o A344357 power_terms = [x**4 for x in range(1, 50)]
%o A344357 for pos in cwr(power_terms, 4):
%o A344357     tot = sum(pos)
%o A344357     keep[tot] += 1
%o A344357 rets = sorted([k for k, v in keep.items() if v == 5])
%o A344357 for x in range(len(rets)):
%o A344357     print(rets[x])
%Y A344357 Cf. A343986, A344353, A344356, A344359, A344365, A344921.
%K A344357 nonn
%O A344357 1,1
%A A344357 _David Consiglio, Jr._, May 15 2021