A377025 Squares and cubes that are not 6th powers.

4, 8, 9, 16, 25, 27, 36, 49, 81, 100, 121, 125, 144, 169, 196, 216, 225, 256, 289, 324, 343, 361, 400, 441, 484, 512, 529, 576, 625, 676, 784, 841, 900, 961, 1000, 1024, 1089, 1156, 1225, 1296, 1331, 1369, 1444, 1521, 1600, 1681, 1728, 1764, 1849, 1936, 2025

Offset

1,1

Comments

Squares and cubes that cannot be written as both a square and a cube.

{A002760}\{A001014}.

A125643 minus the repeated terms.

Links

Table of n, a(n) for n=1..51.

Mathematica

lim=2025; Select[Union[Range[Floor[lim^(1/2)]]^2, Range[Floor[lim^(1/3)]]^3], !IntegerQ[#^(1/6)]&] (* James C. McMahon, Oct 16 2024 *)

Prog

(Python)
from math import isqrt
from sympy import integer_nthroot
def A377025(n):
    def bisection(f, kmin=0, kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return n+x+(integer_nthroot(x, 6)[0]<<1)-integer_nthroot(x, 3)[0]-isqrt(x)
    return bisection(f, n, n)

Crossrefs

Cf. A002760, A125643, A001014.

Sequence in context: A195942 A125643 A002760 * A355062 A355060 A115651

Adjacent sequences: A377022 A377023 A377024 * A377026 A377027 A377028

Keyword

nonn,easy

Author

Chai Wah Wu, Oct 13 2024

Status

approved