A376315 - OEIS

%I #29 Oct 01 2024 10:52:31

%S 2,4,128,256,686,1372,2000,4000,4394,8192,8788,13718,16384,21296,

%T 27436,31250,42592,43904,59582,62500,78608,87808,101306,119164,128000,

%U 157216,159014,194672,202612,235298,256000,281216,318028,332750,389344,390224,453962,470596

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

%C {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 All terms are even.

%H Chai Wah Wu, <a href="/A376315/b376315.txt">Table of n, a(n) for n = 1..897</a>

%o (Python)

%o from itertools import count, islice

%o from sympy import factorint

%o def A376315_gen(startvalue=2): # generator of terms >= startvalue

%o     for k in count(max(startvalue+(startvalue&1),2),2):

%o         f = {p:k*e for p,e in factorint(k).items()}

%o         f[2] += 1

%o         if not any(v%3 for v in f.values()):

%o             yield k

%o A376315_list = list(islice(A376315_gen(),30))

%Y Cf. A376291, A376279.

%K nonn

%O 1,1

%A _Chai Wah Wu_, Sep 20 2024