A380226 10^n-th perfect power.

1, 49, 6400, 804357, 90706576, 9565035601, 979846576384, 99066667994176, 9956760243243489, 997995681331086244, 99907048030216445041, 9995687853365470311364, 999799911985804802176144, 99990714485941936439363361, 9999569051610812899059355921, 999979998395643044466222682969

Offset

0,2

Links

Chai Wah Wu, Table of n, a(n) for n = 0..500

Formula

a(n) = A001597(10^n).

Prog

(Python)
from sympy import mobius, integer_nthroot
def A380226(n):
    m = 10**n
    def bisection(f, kmin=0, kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        kmin = 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 int(m-1+x+sum(mobius(k)*(integer_nthroot(x, k)[0]-1) for k in range(2, x.bit_length())))
    return bisection(f, m, m)

Crossrefs

Cf. A001597.

Sequence in context: A053772 A075416 A127861 * A130416 A006692 A304313

Adjacent sequences: A380223 A380224 A380225 * A380227 A380228 A380229

Keyword

nonn

Author

Chai Wah Wu, Jan 25 2025

Status

approved