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If I define J(x) function as:

def J(x): sum = 0 print(int(log(x)/log(2))) for i in range(1, int(log(x)/log(2)) + 1): sum = sum + 1 / i * prime_pi(x**(1/i)) return(N(sum))

when I try to plot it using:

p = plot(J(x), (x, 1, 20)) show(p)

I get the message: "cannot convert log(x)/log(2) to int"

but if try J function acting on any float number I get a perfect value like:

sage: J(123.456789) 34.0333333333333

I have tried to replace int by floor but with the same result. Any help to solve the plotting problem will be welcome. Thank you.

If I define J(x) J(x) function as:

def J(x):
    sum = 0
    print(int(log(x)/log(2)))
    for i in range(1, int(log(x)/log(2)) + 1):
        sum = sum + 1 / i * prime_pi(x**(1/i))
    return(N(sum))
return(N(sum))

p = plot(J(x), (x, 1, 20))
show(p)
show(p)

cannot convert log(x)/log(2) to int"
int

sage: J(123.456789)
34.0333333333333
34.0333333333333