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A376315 Positive numbers k such that 2*k^k is a cube.

%I A376315 #29 Oct 01 2024 10:52:31
%S A376315 2,4,128,256,686,1372,2000,4000,4394,8192,8788,13718,16384,21296,
%T A376315 27436,31250,42592,43904,59582,62500,78608,87808,101306,119164,128000,
%U A376315 157216,159014,194672,202612,235298,256000,281216,318028,332750,389344,390224,453962,470596
%N A376315 Positive numbers k such that 2*k^k is a cube.
%C A376315 {a(n)} UNION A376291 = positive numbers k such that k^k is not a cube and can be expressed as (x^3 + y^3)/2 for nonnegative integers x, y.
%C A376315 All terms are even.
%H A376315 Chai Wah Wu, <a href="/A376315/b376315.txt">Table of n, a(n) for n = 1..897</a>
%o A376315 (Python)
%o A376315 from itertools import count, islice
%o A376315 from sympy import factorint
%o A376315 def A376315_gen(startvalue=2): # generator of terms >= startvalue
%o A376315     for k in count(max(startvalue+(startvalue&1),2),2):
%o A376315         f = {p:k*e for p,e in factorint(k).items()}
%o A376315         f[2] += 1
%o A376315         if not any(v%3 for v in f.values()):
%o A376315             yield k
%o A376315 A376315_list = list(islice(A376315_gen(),30))
%Y A376315 Cf. A376291, A376279.
%K A376315 nonn
%O A376315 1,1
%A A376315 _Chai Wah Wu_, Sep 20 2024