def p012(N=500):
table = numty.factortable(10**5)
n = 1
while True:
if numdivs(table[n])*numdivs(table[(n+1)/2]) > N:
return n*(n+1)/2
n += 1
if numdivs(table[n/2])*numdivs(table[n+1]) > N:
return n*(n+1)/2
n += 1
def p012(N=500):
table = numty.factortable(10**5)
n = 1
while True:
if numdivs(table[n]) * numdivs(table[(n + 1) / 2]) > N:
return n * (n + 1) / 2
n += 1
if numdivs(table[n / 2]) * numdivs(table[n + 1]) > N:
return n * (n + 1) / 2
n += 1
def p023():
abundant = [n for (n,f) in enumerate(numty.factortable(LIMIT))
if numty.sigma(f) > 2*n > 0]
abundantset = set(abundant)
def check_n(n):
for a in abundant:
if n-a in abundantset:
return False
if n-a < a:
return True
return sum(n for n in range(LIMIT+1) if check_n(n))
def p023():
abundant = [
n for (n, f) in enumerate(numty.factortable(LIMIT))
if numty.sigma(f) > 2 * n > 0
]
abundantset = set(abundant)
def check_n(n):
for a in abundant:
if n - a in abundantset:
return False
if n - a < a:
return True
return sum(n for n in range(LIMIT + 1) if check_n(n))
def p047(N=4, lim=150000):
table = [len(x.keys()) for x in numty.factortable(lim)]
for n in range(len(table)):
if all(table[n+i]>=N for i in range(N)):
return n
return p047(N, 10*lim)
def p069(N=10**6):
table = numty.factortable(N+1)
best = max((1.0*n/phi(n, table[n]), n) for n in range(N+1))
return best[1]
def p072(N=10**6):
table = numty.factortable(N + 1)
return sum(p069.phi(n, table[n]) for n in range(2, N + 1))
def p069(N=10**6):
table = numty.factortable(N + 1)
best = max((1.0 * n / phi(n, table[n]), n) for n in range(N + 1))
return best[1]
def p072(N=10**6):
table = numty.factortable(N+1)
return sum(p069.phi(n, table[n]) for n in range(2,N+1))
