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A099998 Bisection of A001597.

%I A099998 #11 Aug 14 2024 01:50:27
%S A099998 4,9,25,32,49,81,121,128,169,216,243,289,343,400,484,529,625,729,841,
%T A099998 961,1024,1156,1296,1369,1521,1681,1764,1936,2048,2187,2209,2401,2601,
%U A099998 2744,2916,3125,3249,3375,3600,3844,4096,4356,4624,4900,5041,5329,5625,5832
%N A099998 Bisection of A001597.
%t A099998 t = Union@ Flatten@ Table[ n^i, {n, 2, Sqrt[6083]}, {i, 2, Log[n, 6083]}]; t[[2# - 1]] & /@ Range@(Length@t/2)
%o A099998 (Python)
%o A099998 from sympy import mobius, integer_nthroot
%o A099998 def A099998(n):
%o A099998     def f(x): return int((n<<1)-2+x+sum(mobius(k)*(integer_nthroot(x,k)[0]-1) for k in range(2,x.bit_length())))
%o A099998     kmin, kmax = 1,2
%o A099998     while f(kmax) >= kmax:
%o A099998         kmax <<= 1
%o A099998     while True:
%o A099998         kmid = kmax+kmin>>1
%o A099998         if f(kmid) < kmid:
%o A099998             kmax = kmid
%o A099998         else:
%o A099998             kmin = kmid
%o A099998         if kmax-kmin <= 1:
%o A099998             break
%o A099998     return kmax # _Chai Wah Wu_, Aug 14 2024
%K A099998 nonn,easy
%O A099998 1,1
%A A099998 _N. J. A. Sloane_, Nov 20 2004
%E A099998 More terms from _Robert G. Wilson v_, Dec 14 2005