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

2, 4, 128, 256, 686, 1372, 2000, 4000, 4394, 8192, 8788, 13718, 16384, 21296, 27436, 31250, 42592, 43904, 59582, 62500, 78608, 87808, 101306, 119164, 128000, 157216, 159014, 194672, 202612, 235298, 256000, 281216, 318028, 332750, 389344, 390224, 453962, 470596

Offset

1,1

Comments

{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.

All terms are even.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..897

Prog

(Python)
from itertools import count, islice
from sympy import factorint
def A376315_gen(startvalue=2): # generator of terms >= startvalue
    for k in count(max(startvalue+(startvalue&1), 2), 2):
        f = {p:k*e for p, e in factorint(k).items()}
        f[2] += 1
        if not any(v%3 for v in f.values()):
            yield k
A376315_list = list(islice(A376315_gen(), 30))

Crossrefs

Cf. A376291, A376279.

Sequence in context: A009595 A018493 A046035 * A134710 A009073 A326213

Adjacent sequences: A376312 A376313 A376314 * A376316 A376317 A376318

Keyword

nonn

Author

Chai Wah Wu, Sep 20 2024

Status

approved