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179.py
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#!/usr/bin/python
import math,time
def naiti_prostie_i_deliteli_menshe(n, m):
vsen = [True] * (n+1)
# esli vsen[k] == True znachit mi eshyo ne vikinuli k.
# esli vsen[k] == False, znachit mi uzhe vikinuli k.
prostie = []
deliteli = []
# deliteli chisel mi budem sohranyat' v spiske spiskov
# naprimer deliteli[5] eto spisok prostih deliteley 5, to est' [5],
# deliteli[10] = [2, 5]
# Snachala nado inicializirovat' nash spisok deliteli
for i in xrange(m):
deliteli.append([])
koren = math.sqrt(n)
p = 2
while p <= koren:
# Zapominaem nashe prostoe chislo
prostie.append(p)
# Teper' vikidivayem iz spiska vsen, chisla kotorie delyatsya
# na p.
for i in xrange(p, n+1, p):
vsen[i] = False
# chislo i delitsya na p, dobavlyayem p v spisok ego deliteley
if i < m:
deliteli[i].append(p)
chislo = i/p
while True:
if chislo % p == 0:
deliteli[i].append(p)
chislo = chislo / p
else:
break
# Teper' nahodim pervoy chislo v spiske vsen, kotoroe mi eshyo
# ne vikinuli, i zapominaem ego v p.
for i in xrange(p, n+1):
if vsen[i] == True:
p = i
break
# Kogda mi viydem iz cikla, vse ostavshiesya chisla v spiske
# vsen budut prostimi. Ih nado prosto dobavit' v spisok prostie
for i in xrange(p, n+1):
if vsen[i] == True:
prostie.append(i)
if i < m:
for k in xrange(i, m, i):
deliteli[k].append(i)
chislo = k/i
while True:
if chislo % i == 0:
deliteli[k].append(i)
chislo = chislo / i
else:
break
return prostie, deliteli
def nayti_prostie_deliteli(n, prostie, tt, de):
max_de = len(de)
if n in tt:
return [n]
if n < max_de:
return de[n]
if not n in tt:
m = n
deliteli = []
posledniy_index = 0
num_prostih = len(prostie)
while True:
nashli = False
for ind in xrange(posledniy_index, num_prostih):
p = prostie[ind]
if m % p == 0:
m = m / p
deliteli.append(p)
posledniy_index = ind
nashli = True
break
if m in tt:
deliteli.append(m)
return deliteli
if m == 1:
return deliteli
if m < max_de:
deliteli.extend(de[m])
break
if not nashli:
print "Nuzhno bol'she prostih chisel, etih ne hvatilo"
return []
return deliteli
def vse_deliteli(prostie_del):
dd = {}
for d in prostie_del:
if d not in dd:
dd[d] = 1
else:
dd[d] += 1
#print dd
factors = []
for d, c in dd.iteritems():
if c == 1:
factors.append([d])
else:
factors.append([])
for i in xrange(1, c + 1):
factors[-1].append(pow(d, i))
#print factors
n = len(factors)
all_dels = [1]
for ind in xrange(1, pow(2,n)):
#print "INDEX IS", ind
count = 0
dels = [1]
while ind > 0:
if ind % 2 == 1:
orig_dels_len = len(dels)
last = len(factors[count]) - 1
for f in xrange(last + 1):
if f == last:
#print "doing last", dels
for j in xrange(orig_dels_len):
dels[j] *= factors[count][f]
#print "done last", dels
else:
#print "doing normal", dels
for j in xrange(orig_dels_len):
dels.append(dels[j] * factors[count][f])
#print "done normal", dels
count += 1
ind = ind >> 1
#print "DONE THIS INDEX", dels
all_dels.extend(dels)
return all_dels
#print "ans", vse_deliteli([2])
#print "ans", vse_deliteli([2, 2])
#print "ans", vse_deliteli([2, 2, 2])
#print "ans", vse_deliteli([3, 2])
#print "ans", vse_deliteli([3, 2, 2])
#print "ans", vse_deliteli([3, 2, 2, 2])
#print "ans", vse_deliteli([3, 3, 2, 2])
#test_vse_deliteli()
def nayti_chislo_deliteley(prostie_deliteli):
per = prostie_deliteli[0]
p = 0
vt = -1
nov = []
suma = 1
for i in prostie_deliteli:
vt+=1
if not per == i:
per = prostie_deliteli[vt]
nov.append(prostie_deliteli[p:vt])
p = vt
nov.append(prostie_deliteli[p:])
for ch in nov:
suma *= (len(ch)+1)
return suma
chislo_deli = {}
#3798207594720
pros, de = naiti_prostie_i_deliteli_menshe(10**7+1, 10**7+1)
ad = set(pros)
for i in xrange(2,10**7+1):
if i % 200000 == 0:
print i
a = nayti_prostie_deliteli(i, pros, ad, de)
eeee = nayti_chislo_deliteley(a)
chislo_deli[i] = eeee
kal = 0
for i in xrange(2,10**7):
if i % 500000 == 0:
print i
if chislo_deli[i] == chislo_deli[i+1]:
kal +=1
print kal
#pros, de = naiti_prostie_i_deliteli_menshe(64000000, 15000000)
#ad = set(pros)
#s = 0
#for i in xrange(2,64000000):
# if i % 100000 == 0:
# print i
# a = nayti_prostie_deliteli(i, pros, ad, de)
# d = summa_kvadratov_deliteley(a)
# if math.sqrt(d) % 1 == 0:
# if int(math.sqrt(d)) ** 2 == d:
# s += i
#print s
#528