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A099997 Bisection of A001597.

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