Lots of stuff happening in the past week. Let me begin with that news which should come as a blow to storage enthusiasts. The HD-DVD format is going forever. Toshiba says it will no longer create HD-DVD players/records. Now, I liked the HD-DVD format for its ECMAScript support. Well thats over. Then the US blew up a satellite, China’s pissed and wants to know more about the mission, my board exams are getting closer ( bleagh! ). Anyway, here is an update on my “work” in the past week.
Oh BTW, while solving a question related to the Fibonacci sequence, I found a supercool formula - the Binet’s formula. Let the greatest integer function be represented by “[]”
f(x) = [x]
let F represent the Fibonacci sequence. The Binet’s formula states that
F(n) = [{(1 + sqrt(5))^n}-{(1-sqrt(5))^n} / (2^n * sqrt(5))]
There ! Now you can solve that Fibonacci problem in the project euler archives.
I solved another sum. Here is the question:
Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n). If d(a) = b and d(b) = a, where a ? b, then a and b are an amicable pair and each of a and b are called amicable numbers.For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220. Evaluate the sum of all the amicable numbers under 10000.
Here is the solution:
#!/usr/bin/env python
#Amicable numbers
def makeFactors(number):
factor_list = []
if number % 2 == 0:
for i in range(1, number / 2 + 1):
if number % i == 0:
factor_list.append(i)
else:
continue
else:
for i in range(1, (number + 1)/2):
if number % i == 0:
factor_list.append(i)
else:
continue
return factor_list
def checkAmicable(number):
factor_list = makeFactors(number)
factor_sum = sum(factor_list)
new_factor_list = makeFactors(factor_sum)
new_factor_sum = sum(new_factor_list)
if new_factor_sum == number and factor_sum != number:
return True
else:
return False
amicable_list = []
for number in range(0, 10001):
if checkAmicable(number):
amicable_list.append(number)
else:
continue
print sum(amicable_list)
Thats it for now, goodbye !
1 comment so far ↓
You might want to use latex to render the math equations, that will be much easier to read.
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