v = load('http://wstein.org/home/wstein/db/ellcurve_counts/ellcurve_counts_100000000.sobj')
Attempting to load remote file: http://wstein.org/home/wstein/db/ellcurve_counts/ellcurve_counts_1000000\ 00.sobj Loading: [..................................................] Attempting to load remote file: http://wstein.org/home/wstein/db/ellcurve_counts/ellcurve_counts_100000000.sobj Loading: [..................................................] |
# enumerate squarefree integers <= 10^8
M=10^8+1
p=prime_range(sqrt(M))
p=[i^2 for i in p]
sqf=range(M)
for i in p:
for j in range(i,M,i):
sqf[j]=0
|
|
a=[]
m=M//200
sum1=0
sum2=0
for i in range(1,M):
if sqf[i]:
sum1+=v[i]
else:
sum2+=v[i]
if not i%m:
a.append((i,sum1/(sum1+sum2)))
|
|
line(a)
|
|
B=[]
p=p[:15]
for q in p:
b=[]
sum1=0
sum2=0
for i in range(1,M):
if i%q:
sum1+=v[i]
else:
sum2+=v[i]
if not i%m:
b.append((i,sum1/(sum1+sum2)))
B.append(b)
|
|
The second plot is an overlay of the graphs for f_p you described in the 3rd part of your original post for p<50. The f_p -> 1 as p->oo, at least as the graphs would have you believe.
sum(line(B[i]) for i in range(15))
|
|
|
|