18.783 Problem Set 5 Problem 5.ipynb

Kernel: SageMath 9.2

def F(a): return dickman_rho(1/a)

def G(a,b): return F(a) + numerical_integral(lambda x: F(a/(1-x))/x,a,b)[0]

# in the table below, utab[i] minimizes M^(1/u)/G(1/u,2/u) for M=2^(10*i)
utab=[2.000, 2.721, 3.200, 3.611, 3.929, 4.237, 4.501, 4.740, 4.969, 5.184, 5.382, 5.569, 5.751, 5.925, 6.091, 6.250, 6.404, 6.553, 6.698, 6.839, 6.975]