A380226 - OEIS

%I #26 May 26 2026 01:04:57

%S 1,49,6400,804357,90706576,9565035601,979846576384,99066667994176,

%T 9956760243243489,997995681331086244,99907048030216445041,

%U 9995687853365470311364,999799911985804802176144,99990714485941936439363361,9999569051610812899059355921,999979998395643044466222682969

%N 10^n-th perfect power.

%H Chai Wah Wu, <a href="/A380226/b380226.txt">Table of n, a(n) for n = 0..500</a>

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

%o (Python)

%o from sympy import mobius, integer_nthroot

%o def A380226(n):

%o     m = 10**n

%o     def bisection(f,kmin=0,kmax=1):

%o         while f(kmax) > kmax: kmax <<= 1

%o         kmin = kmax>>1

%o         while kmax-kmin > 1:

%o             kmid = kmax+kmin>>1

%o             if f(kmid) <= kmid:

%o                 kmax = kmid

%o             else:

%o                 kmin = kmid

%o         return kmax

%o     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())))

%o     return bisection(f,m,m)

%Y Cf. A001597.

%K nonn

%O 0,2

%A _Chai Wah Wu_, Jan 25 2025