A099997 Bisection of A001597.

1, 8, 16, 27, 36, 64, 100, 125, 144, 196, 225, 256, 324, 361, 441, 512, 576, 676, 784, 900, 1000, 1089, 1225, 1331, 1444, 1600, 1728, 1849, 2025, 2116, 2197, 2304, 2500, 2704, 2809, 3025, 3136, 3364, 3481, 3721, 3969, 4225, 4489, 4761, 4913, 5184, 5476

Offset: 1

Author

N. J. A. Sloane, Nov 20 2004

Keywords

• nonn
• easy

Programs

Mathematica

t = Union@ Flatten@ Join[{1}, Table[ n^i, {n, 2, Sqrt[5775]}, {i, 2, Log[n, 5775]}]]; t[[2# - 1]] & /@ Range@(Length@t/2) (* Robert G. Wilson v *)

Python

from sympy import mobius, integer_nthroot
def A099997(n):
    def f(x): return int((n<<1)-3+x+sum(mobius(k)*(integer_nthroot(x,k)[0]-1) for k in range(2,x.bit_length())))
    kmin, kmax = 1,2
    while f(kmax) >= kmax:
        kmax <<= 1
    while True:
        kmid = kmax+kmin>>1
        if f(kmid) < kmid:
            kmax = kmid
        else:
            kmin = kmid
        if kmax-kmin <= 1:
            break
    return kmax # Chai Wah Wu, Aug 14 2024

Extensions

More terms from Robert G. Wilson v, Dec 14 2005