A099998 Bisection of A001597.

4, 9, 25, 32, 49, 81, 121, 128, 169, 216, 243, 289, 343, 400, 484, 529, 625, 729, 841, 961, 1024, 1156, 1296, 1369, 1521, 1681, 1764, 1936, 2048, 2187, 2209, 2401, 2601, 2744, 2916, 3125, 3249, 3375, 3600, 3844, 4096, 4356, 4624, 4900, 5041, 5329, 5625, 5832

Offset

1,1

Links

Table of n, a(n) for n=1..48.

Mathematica

t = Union@ Flatten@ Table[ n^i, {n, 2, Sqrt[6083]}, {i, 2, Log[n, 6083]}]; t[[2# - 1]] & /@ Range@(Length@t/2)

Prog

(Python)
from sympy import mobius, integer_nthroot
def A099998(n):
    def f(x): return int((n<<1)-2+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

Crossrefs

Sequence in context: A163836 A175085 A182120 * A360902 A365003 A367406

Adjacent sequences: A099995 A099996 A099997 * A099999 A100000 A100001

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 20 2004

Extensions

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

Status

approved