= P1*1 P2*₂. -Prk. et g = gcd(k₁, k2.... k) and m, = k₁/g. he function F is defined as: F(n) = P11 P22- Tow we have to summing up the value of this function for the first N natural r P.m
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- Program in python There is function F. Give an integer n (n ≥ 2), consider the prime factorization n=pi³1 P2²₂ Let g = ged(ky, k₂. k) and m, = k/g The function F is defined as F(n) = P11 P2" Prr 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 given value of N: F(2) + F(3)+...+F(N) As the above sum can be extremely large Example if F(125)=5, thus the answer for this is by five more than for the previous one.Program in python There is function F. Give an integern (n 2 2), consider the prime factorization n p1 p Let g gcd(k, k2, . k) and m, k, /g. The function F is defined as: F(n)=p1", p22 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 given value of N F(2) + F(3) +.+ F(N).As the above sum can be extremely large Example if F(125) = 5, thus the answer for this is by five more than for the previous one.Program in python .There is function F. Give an integer n (n > 2), consider the prime factorization n Let 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 given value of N: F(2)+ F(3) + ... + F(N).As the above sum can be extremely large Example if F(125) = 5, thus the answer for this is by five more than for the previous one.
- In loop functions.py, define a function named permutations that takes two paramters, n and r, in that order. This function returns the number of different permutations of length r from set of size n. Essentially to calculate these permutations, the function should compute the product (n - r+1)*(n-r+2)*(n-r+3)*...*(n-2)*(n-1) or n!/(n-r)!. No if statements or built in math functions should be used. For or while loops are best reccomended.In a Python function, represent the mathematical functionf(x)= exp(-x2) cos(2*pi*x) on a mesh consisting of q + 1 equally spaced points on [-1,1], and return 1) the interpolated function value at x = -0.45 and 2) the error in the interpolated value.Call the function and write out the error for q = 2,4,8,16Write a python function sqr(n) that returns the square of its parameter n for example: Test Result print(sqr(-3)) 9 print(sqr(11)) 121
- Given a vector of real numbers r = (r1, V2, ..., rn). We can standardize the vector using the formulation: V; = "im, where m is the ri-m mean of the vector r, and s is the standard deviation of r. The vector v = (V1, V2, . , Un) will be the scaled vector. ... 9 Write a Python function scale_vec(r) that takes the vector r as input and returns the scaled vector v. Sample inputs and outputs: • Input: np.array([1, 3, 5]), output: [-1.22474487 0. 1.22474487] Input: np.array([3.3, 1.2, -2.7, −0.6]), output: [1.35457092 0.40637128 -1.35457092 -0.40637128] Hint: Use numpy.mean and numpy.std with default parameters. [ ] # Write your function here Let's test your function. [ ] import numpy as np print (scale_vec(np.array ( [1, 3, 5]))) print (scale_vec(np.array([3.3, 1.2, -2.7, -0.6])))Let f be a function that takes some natural number n, and adds the value that n takes when its digits are reversed. For example, for n = 178 we have: f(178) = 178 +871 = 1049 If we keep iterating this value, we get: f(1049) = 1049 + 9401 = 10450 f(10450) = 10450 + 05401 = 15851 Notice that for the starting value n = 178, we eventually got a palindromic number 15851 (i.e. a value that reads the same backward as forwards). Write a function lychrel (n) that accepts any natural number n, and returns a list of iterates [n, f(n),...] of n under the function f that only terminates as soon as it reaches a palindromic value.USE PYTHON Given a square matrix, calculate the absolute difference between the sums of its diagonals. For example, the square matrix is shown below: 1 2 3 4 5 6 9 8 9 The left-to-right diagonal = 1+5+9=15. The right to left diagonal = 3+5+9 = 17 Their absolute difference is |15-17| = 2 Provide python code for the function DiagonalDifference(). It must return an integer representing the absolute diagonal difference. DiagonalDifference takes the following parameter: arr: a 2D array of integers.
- Write a function sumDigits, that accepts a positive integer n and returns the sum of the digits in that integer; thus, sumDigits(34) would return 7 (e.g., 3+4). Use the techniques from the roman numeral problem to extract the digitsAbraham Series to Compute Write a well-documented Python program, hmwk4Q2.py, that calculates. Construct a function abr_pi.py(N) accepts an integer N and returns an estimate of computing the Abraham Series using N terms. The series is: [2(1) 3ần 2n + 1 12=0 Have the main() call upon your function for various values of N to ensure it is correctly working. π =Write a Python function power(f,n) that takes a function f and an integer n, and returns a function that applies the function f to its argument n times. For example: power(f,0)(x) = x # apply f over x zero time = no application power(f,2)(x) = f(f(x)) # apply f over x twice, same as twice(f) power(f,5)(x) = f(f(f(f(f(x))))) # apply f over x five times If we have the function: def incr(x): return x+1, and x=5, then the above three calls would be, power(incr,0)(5) # => 5 power(incr,2)(5) # => 7 (apply incr over 5 twice) power(incr,5)(5) # => 10 (apply incr over 5 five times)