Program in python .There is function F. Give an integer n (n > 2), consider the prime factorizationnLet g = gcd(k1, k2, ... k,) and m; = k; / g.The function F is defined as: F(n)=p1™1·P22·Pr"r-Now, we have to summing up the value of this function for the first N natural numbers, we have w to evaluate the following expression for a givenvalue of N: F(2)+ F(3) + ... + F(N).As the above sum can be extremely largeExample if F(125) = 5, thus the answer for this is by five more than for the previous one.

Prime factors of a number are those prime numbers which on multiplying together we get original…

Answered: here is function F. Give an integer n…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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In rare cases, it's not such a great idea to "round prematurely." Consider the following function: ALG3(n): count := 0 for i = 0,..., n for j = 1,..., 2¹ return count count := count +1 (a) Give big-O estimates for the number of iterations of each loop, and use those estimates to give a big-O estimate for the return value count. (b) Give an exact formula for the return value count, and then simplify it using big-0 notation. (Hint: you might need the formula for the sum of a geometric series.) Is this better than your answer in part (a)?
The question describes a function S(k) which is defined as the sum of the positive divisors of a positive integer k, minus k itself. The function S(1) is defined as 1, and for any positive integer k greater than 1, S(k) is calculated as S(k) = σ(k) - k, where σ(k) is the sum of all positive divisors of k. Some examples of S(k) are given: S(1) = 1 S(2) = 1 S(3) = 1 S(4) = 3 S(5) = 1 S(6) = 6 S(7) = 1 S(8) = 7 S(9) = 4 The question then introduces a recursive sequence a_n with the following rules: a_1 = 12 For n ≥ 2, a_n = S(a_(n-1)) Part (a) of the question asks to calculate the values of a_2, a_3, a_4, a_5, a_6, a_7, and a_8 for the sequence. Part (b) modifies the sequence to start with a_1 = k, where k is any positive integer, and the same recursion formula applies: for n ≥ 2, a_n = S(a_(n-1)). The question notes that for many choices of k, the sequence a_n will eventually reach and remain at 1, but this is not always the case. It asks to find, with an explanation, two specific…
Let f (n) and g(n) be positive functions (for any n they give positive values) and f (n) = O(g(n)).Prove or disprove the following statement:
(1) Next try writing a simple function euler_phi to compute Euler's function. This should take an integer n, and for each i from 1 to n − 1, adds one to a counter each time we have gcd(i, n) = 1 (i.e., for each i which is relatively prime to n). Is this code quicker than semiprime_factorisation1? That is, if we wanted to compute (n) for n semiprime, is it quicker to use euler_phi directly, or to use semiprime_factorisation and then calculate (n) = (p − 1)(q − 1)? (2) It's not too hard to see that a faster semiprime factorisation function is trial division, also called direct search factorisation. This simply involves dividing n by each integer from 2 to [√n], to find integers which divide n exactly (that is, have a remainder of zero). Write a function semiprime_factorisation2 which takes an integer n, which is a semiprime (i.e., is the product of two primes p and q), and returns both p and q. Remember to use integer division here, with //. Test your function on some values of n = pq.…
Give asymptotic upper and lower bounds for each of the following recurrences. Justify your answer.
Which function grows faster f(n) = log 2n or g(n) = n0.3log3n
for i=1 to n/2: for j-i to n-i : for k=1 to j do print("hello") Let T(n) denote the number of times "hello" is printed as a function of n. 1- Find a function f(n) -> T(n)=0(f(n)) 2- Explain T(n) as three nested summations, and simplify them by step by step
Use de l'Hopital's rule to find the limit as n tends to infinity of(log log n) a / log n, where a > 0 is an arbitrary positive constant.
suppose a,b, and c are odd integers. Prove that a+b+c is odd
Let f (f(n) and g(n)) be asymptotically nonnegative functions. Using the basic definition of Θ notation, prove that max(f(n), g(n)) = Θ(f(n) + g(n)),

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