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Bisection of A001597.
1

%I #11 Aug 14 2024 01:50:27

%S 4,9,25,32,49,81,121,128,169,216,243,289,343,400,484,529,625,729,841,

%T 961,1024,1156,1296,1369,1521,1681,1764,1936,2048,2187,2209,2401,2601,

%U 2744,2916,3125,3249,3375,3600,3844,4096,4356,4624,4900,5041,5329,5625,5832

%N Bisection of A001597.

%t t = Union@ Flatten@ Table[ n^i, {n, 2, Sqrt[6083]}, {i, 2, Log[n, 6083]}]; t[[2# - 1]] & /@ Range@(Length@t/2)

%o (Python)

%o from sympy import mobius, integer_nthroot

%o def A099998(n):

%o 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 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 1,1

%A _N. J. A. Sloane_, Nov 20 2004

%E More terms from _Robert G. Wilson v_, Dec 14 2005