A099997 - OEIS

%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