%I #12 Aug 14 2024 01:50:42
%S 1,8,16,27,36,64,100,125,144,196,225,256,324,361,441,512,576,676,784,
%T 900,1000,1089,1225,1331,1444,1600,1728,1849,2025,2116,2197,2304,2500,
%U 2704,2809,3025,3136,3364,3481,3721,3969,4225,4489,4761,4913,5184,5476
%N Bisection of A001597.
%t 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_ *)
%o (Python)
%o from sympy import mobius, integer_nthroot
%o def A099997(n):
%o 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())))
%o kmin, kmax = 1,2
%o while f(kmax) >= kmax:
%o kmax <<= 1
%o while True:
%o kmid = kmax+kmin>>1
%o if f(kmid) < kmid:
%o kmax = kmid
%o else:
%o kmin = kmid
%o if kmax-kmin <= 1:
%o break
%o return kmax # _Chai Wah Wu_, Aug 14 2024
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Nov 20 2004
%E More terms from _Robert G. Wilson v_, Dec 14 2005