A376279 Numbers k such that k^k is a cube.

0, 1, 3, 6, 8, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 64, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 125, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165, 168

Offset

1,3

Comments

Strict subsequence of A267415. For instance, 76, 112, 172, 364, 427, 532 are not terms of this sequence, but are terms of A267415.

Links

Table of n, a(n) for n=1..61.

Chai Wah Wu, Algorithms for Complementary Sequences, Integers (2025) Vol. 25, Art. No. A95. See p. 21. (Because of a misprint, the article refers to A376379 instead of A376279.)

Formula

k is a term if and only if k is a multiple of 3 or k is a cube.

Maple

q:= n-> andmap(i-> irem(n*i[2], 3)=0, ifactors(n)[2]):
select(q, [$0..200])[];  # Alois P. Heinz, Sep 19 2024

Mathematica

Join[{0}, Select[Range[170], IntegerQ[#^(#/3)] &]] (* Stefano Spezia, Sep 18 2024 *)

Prog

(Python)
from sympy import integer_nthroot
def A376279(n):
    def f(x): return n-1+x-x//3-integer_nthroot(x, 3)[0]+integer_nthroot(x//27, 3)[0]
    m, k = n-1, f(n-1)
    while m != k: m, k = k, f(k)
    return m
(Python)
from itertools import count, islice
from sympy import integer_nthroot
def A376279_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda k:not k%3 or integer_nthroot(k, 3)[1], count(max(startvalue, 0)))
A376279_list = list(islice(A376279_gen(), 30))
(PARI) isok(k) = ispower(k^k, 3); \\ Michel Marcus, Sep 18 2024
(PARI) is(n)=n%3==0 || ispower(n, 3) \\ Charles R Greathouse IV, Nov 04 2025

Crossrefs

Union of A000578 and A008585.

Cf. A267415, A371587.

Sequence in context: A189637 A182338 A267415 * A140516 A310140 A231006

Adjacent sequences: A376276 A376277 A376278 * A376280 A376281 A376282

Keyword

nonn,easy

Author

Chai Wah Wu, Sep 18 2024

Status

approved