wai4u/hcn.csv

## hcn.csv

          
            
            <
            n
            d(n)
            factorize

            
              0
              10^3
              840
              32
              2^3·3·5·7

            
              1
              10^6
              720720
              240
              2^4·3^2·5·7·11·13

            
              2
              10^9
              735134400
              1344
              2^6·3^3·5^2·7·11·13·17

            
              3
              10^12
              963761198400
              6720
              2^6·3^4·5^2·7·11·13·17·19·23

            
              4
              10^15
              866421317361600
              26880
              2^6·3^4·5^2·7·11·13·17·19·23·29·31

            
              5
              10^18
              897612484786617600
              103680
              2^8·3^4·5^2·7^2·11·13·17·19·23·29·31·37

## hcn.py
def primetable(n):
	isp=[True]*n
	isp[0]=isp[1]=False
	for i in range(n):
		if i*i>=n:break
		if not isp[i]:continue
		for j in range(i*i,n,i):isp[j]=False
	return isp
def primes(n):
	return [i for i,f in enumerate(primetable(n))if f]
def hcn(n=10**150):
	assert n<=10**500
	A=[(1,1,[])]
	for i,p in enumerate(primes(1104)):
		B=[]
		for a in A:
			B.append(a)
			x,d,e=a
			if len(e)<i:continue
			for j in range(1,e[i-1]+1 if i>0 else 17):
				x*=p
				if x>n:break
				B.append((x,d*(j+1),e+[j]))
		B.sort()
		A=A[:1]
		for a in B:
			if a[1]>A[-1][1]:A.append(a)
	return A
import pandas as pd
ls=[None]*20
data=[]
for x in hcn(10**18):
	ls[len(str(x[0]))]=x
ps=primes(100)
for i in range(3,19,3):
	x,d,e=ls[i]
	e='·'.join(str(ps[i])+('' if c==1 else f'^{c}')for i,c in enumerate(e))
	data.append((f'10^{i}',x,d,e))
df=pd.DataFrame(data=data,columns=('<','n','d(n)','factorize'))
print(df)
df.to_csv('hcn.csv')
	<	n	d(n)	factorize
0	10^3	840	32	2^3·3·5·7
1	10^6	720720	240	2^4·3^2·5·7·11·13
2	10^9	735134400	1344	2^6·3^3·5^2·7·11·13·17
3	10^12	963761198400	6720	2^6·3^4·5^2·7·11·13·17·19·23
4	10^15	866421317361600	26880	2^6·3^4·5^2·7·11·13·17·19·23·29·31
5	10^18	897612484786617600	103680	2^8·3^4·5^2·7^2·11·13·17·19·23·29·31·37
	def primetable(n):
	isp=[True]*n
	isp[0]=isp[1]=False
	for i in range(n):
	if i*i>=n:break
	if not isp[i]:continue
	for j in range(i*i,n,i):isp[j]=False
	return isp
	def primes(n):
	return [i for i,f in enumerate(primetable(n))if f]
	def hcn(n=10**150):
	assert n<=10**500
	A=[(1,1,[])]
	for i,p in enumerate(primes(1104)):
	B=[]
	for a in A:
	B.append(a)
	x,d,e=a
	if len(e)<i:continue
	for j in range(1,e[i-1]+1 if i>0 else 17):
	x*=p
	if x>n:break
	B.append((x,d*(j+1),e+[j]))
	B.sort()
	A=A[:1]
	for a in B:
	if a[1]>A[-1][1]:A.append(a)
	return A
	import pandas as pd
	ls=[None]*20
	data=[]
	for x in hcn(10**18):
	ls[len(str(x[0]))]=x
	ps=primes(100)
	for i in range(3,19,3):
	x,d,e=ls[i]
	e='·'.join(str(ps[i])+('' if c==1 else f'^{c}')for i,c in enumerate(e))
	data.append((f'10^{i}',x,d,e))
	df=pd.DataFrame(data=data,columns=('<','n','d(n)','factorize'))
	print(df)
	df.to_csv('hcn.csv')