def calc():
mydiv = Divisors(100000000)
searching = True
number = 3
t = 2
while searching:
t += 1
number += t
factors = mydiv.prime_factors(number)
num_of_fac = 1
for ele in factors:
num_of_fac *= ele[1] + 1
if num_of_fac > 500:
searching = False
return number
def calc(n):
ammic = []
mydiv = Divisors(n)
for i in range(2, n):
j = sum_divis(i, mydiv)
if sum_divis(j, mydiv) == i and i != j:
ammic.append(i)
result = 0
for ele in ammic:
if ele < n:
result += ele
return result
from eulerlib import Divisors
from math import gcd
divi = Divisors()
n = 1
r = 0
for i in range(1, n):
for j in range(i + 1, n + 1):
r += gcd(i, j)
print(r)
k = 1
p = 7
r = 0
for l in range(k + 1):
for d in range(l + 1):
r += (p**d) * divi.phi(p**(l - d))
print(r)
from eulerlib import Divisors
from math import gcd
N = 1000001
divobj = Divisors(N)
def funcion(n):
global d
divis = divobj.divisors(n)
r = 0
# print("divis {}".format(divis))
for d in divis[:]:
r += d * divobj.phi(n // d)
# print("d {} phi {} es {}".format(d,n//d,divobj.phi(n//d)))
return int(r)
for i in range(1, N + 1):
# print("f[{}]={} phi {}".format(i,funcion(i),int(divobj.phi(i))))
print("f[{}]={}".format(i, funcion(i)))
# -*- coding: utf-8 -*-
"""
Created on Sun Oct 20 12:24:06 2019
@author: infoplus
"""
MAXNUM = 28123
from eulerlib import Divisors
mydiv = Divisors(MAXNUM+1)
#def is_abundant(i):
# return i < sum(mydiv.divisors(i)[:-1])
def divisorsum(n):
return sum(i+int(n/i) for i in range(1,int(n**0.5)+1))
def is_abundant(i):
return i < (divisorsum(i)-i)
numbers = [i for i in range(MAXNUM+1)]
abundants = [i for i in numbers[1:] if is_abundant(i)]
for i in range(MAXNUM+1):
for j in range(i+1):
tmp = abundants[i]+abundants[j]
if tmp<=MAXNUM:
numbers[tmp]=0
print(sum(numbers))
#!/Library/Frameworks/Python.framework/Versions/3.7/bin/python3
from eulerlib import Divisors
from functools import reduce
import sys
d = Divisors(1E5)
for line in sys.stdin:
if line:
n = int(line)
phi = int(d.phi(n))
# print("n {} phi {}".format(n,phi))
print(phi >> 1)
import sys
sys.path.append(
"c:\\users\\conrad pearson\\appdata\\local\\programs\\python\\python36-32\\lib\\site-packages"
)
#eulerlib is useful for finding divisors
#but too slow on this scale
from eulerlib import Divisors
#this sets max value of which divisors can be found
div = Divisors(100000000)
#initialize our triangle number and other useful variables
triangle = 0
max_div = 0
i = 0
#iterate and find next triangle number until condition is met
while max_div < 500:
i += 1
triangle += i
max_div = len(div.divisors(triangle))
print(triangle)
#expected value: 76576500
from eulerlib import Divisors
from functools import reduce
d=Divisors()
#print(d.phi(123))
n=10
i=1
r=0
for i in range(1,n+1):
phi=d.phi(i)
ci=n//i
print("i {} ci {} phi {}".format(i,ci,phi))
r+=phi*(ci*(ci-1))//2
print(r)
n=200000
i=1
r=0
while(i<=n):
la=n//(n//i)
ci=n//i
print("i {} ci {} la {} rang {}".format(i,ci,la,list(range(i,la+1))))
suma_phi=reduce(lambda x,y:x+d.phi(y),range(i,la+1),0)
print("phis {} {}".format(list(range(i,la+1)), list(map(d.phi,range(i,la+1)))))
print("sum phi {}".format(suma_phi))
r+=((ci*(ci-1))//2)*suma_phi
i=la+1
print(r)