A perfect number is a positive integer that is equal to the sum of its positive divi- sors except the number itself. The first two perfect numbers are 6 and 28 since 6 =1+2+3 and 28 1+2+4 +7 +14. Write a computer program that finds the first four perfect numbers.
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- P1 P2 P3 P4 A pentagonal number is one that corresponds to dots arranged into a pentagon. Above are the first four pentagonal numbers and their pentagons. The pentagonal number PN has sides made of N dots. When you count the dots for a pentagonal number, include the dots for the inner pentagons. So to figure out how many dots PN has, find out how many P(N-1) has and add the dots for the new sides of size N. P1 = 1, P2 = 5, P3 = 12, P4 = 22 Figure out a recursive formula for PN and then write a function that implements it. That is, implement pentagonal() using recursion. pentagonal(1) -> 1 pentagonal(2) -> 5 pentagonal(3) -> 12An integer is called squarefree if it is not divisible by any perfect squares other than 1. For instance, 42 is squarefree because its divisors are 1, 2, 3, 6, 7, 21, and 42, and none of those numbers (except 1) is a perfect square. On the other hand, 45 is not squarefree because it is divisible by 9, which is a perfect square. Write an algorithm that asks the user to enter a positive integer n and tells them if it is squarefree or not.A prime number is called a Mersenne prime if it can be writtenin the form 2p - 1 for some positive integer p. Write a program that findsall Mersenne primes with p ≤100 and displays the output as shown below.(Hint: You have to use BigInteger to store the number because it is too big tobe stored in long. Your program may take several hours to run.) p 2^p – 1---------------------2 33 75 31...
- If you add up all the digits in 468, you get 4 + 6 + 8 = 18. The square and cube of 468 are 219024 and 102503232, respectively. Interestingly, if you add up the digits of the square or cube, you get 18 again. Are there other integers that share this property? Write a program that lists all positive integers k less than 1000 such that the three numbers k, k2, and k3 have digits that add up to the same number.You are given an integer, N. Your task is to print an alphabet rangoli of size N. (Rangoli is a form of Indian folk art based on creation of patterns.) Different sizes of alphabet rangoli are shown below: #size 3 ----C---- --c-b-c-- c-b-a-b-c --c-b-c-- ----C---- #size 5 ------e-d-e-- ----e-d-c-d-e---- --e-d-c-b-c-d-e-- e-d-c-b-a-b-c-d-e --e-d-c-b-c-d-e-- ----e-d-c-d-e---- e-d-e---- ---- #size 10 --j- -j-i-j- --j-i-h-i-j-- ---j-i-h-g-h-i-j- --j-i-h-g-f-g-h-i-j- -j-i-h-g-f-e-f-g-h-i-j-- ------j-i-h-g-f-e-d-e-f-g-h-i-j-- ----j-i-h-g-f-e-d-c-d-e-f-g-h-i-j--- --j-i-h-g-f-e-d-c-b-c-d-e-f-g-h-i-j-- j-i-h-g-f-e-d-c-b-a-b-c-d-e-f-g-h-i-j --j-i-h-g-f-e-d-c-b-c-d-e-f-g-h-i-j-- ----j-i-h-g-f-e-d-c-d-e-f-g-h-i-j-- -j-i-h-g-f-e-d-e-f-g-h-i-j- -j-i-h-g-f-e-f-g-h-i-j- ---j-i-h-g-f-g-h-i-j- --j-i-h-g-h-i-j- -j-i-h-i-j- j-i-j- The center of the rangoli has the first alphabet letter a, and the boundary has the Nth alphabet letter (in alphabetical order). Eunction DescrintionYou are given an integer, N. Your task is to print an alphabet rangoli of size N. (Rangoli is a form of Indian folk art based on creation of patterns.) Different sizes of alphabet rangoli are shown below: #size 3 ----c---- --c-b-c-- c-b-a-b-c --c-b-c-- ----C---- #size 5 --------e-- ------e-d-e--- ----e-d-c-d-e--- --e-d-c-b-c-d-e-- e-d-c-b-a-b-c-d-e --e-d-c-b-c-d-e-- ----e-d-c-d-e-- ------e-d-e--- #size 10 -j- -j-i-j-- --------j-i-h-i-j- ---------j-i-h-g-h-i-j-- ---------j-i-h-g-f-g-h-i-j-- --------j-i-h-g-f-e-f-g-h-i-j-- ------j-i-h-g-f-e-d-e-f-g-h-i-j--- ----j-i-h-g-f-e-d-c-d-e-f-g-h-i-j--- --j-i-h-g-f-e-d-c-b-c-d-e-f-g-h-i-j-- j-i-h-g-f-e-d-c-b-a-b-c-d-e-f-g-h-i-j --j-i-h-g-f-e-d-c-b-c-d-e-f-g-h-i-j-- ----j-i-h-g-f-e-d-c-d-e-f-g-h-i-j---- ------j-i-h-g-f-e-d-e-f-g-h-i-j--- --------j-i-h-g-f-e-f-g-h-i-j- --j-i-h-g-f-g-h-i-j-- --j-i-h-g-h-i-j- --j-i-h-i-j- -j-i-j-- -j- The center of the rangoli has the first alphabet letter a, and the boundary has the Nth alphabet letter (in…
- Mailbox Mnemonic Code IN STO 90 IN ADD 90 STO 90 IN SUB 90 OUT COB 00 01 02 1. The following Little Man program is supposed to add two input numbers, subtract a third input number from the sum, and output the result, i.e., OUT = IN1 + IN2 – IN3 03 04 05 06 07 08 Numeric Code 901 390 901 190 390 901 290 902 000 What is wrong with this program? Modify the program so that it produces the correct result.strobogrammatic number is a number that looks the same when rotated 180 degrees (looked at upside down). Find all strobogrammatic numbers that are of length = n. For example, Given n = 2, return ["11","69","88","96"]. def gen_strobogrammatic(n): Given n, generate all strobogrammatic numbers of length n. :type n: int :rtype: List[str] return helper(n, n) def helper(n, length): if n == 0: return [™"] if n == 1: return ["1", "0", "8"] middles = helper(n-2, length) result = [] for middle in middles: if n != length: result.append("0" + middle + "0") result.append("8" + middle + "8") result.append("1" + middle + "1") result.append("9" + middle + "6") result.append("6" + middle + "9") return result def strobogrammatic_in_range(low, high): :type low: str :type high: str :rtype: int res = count = 0 low_len = len(low) high_len = len(high) for i in range(low_len, high_len + 1): res.extend(helper2(i, i)) for perm in res: if len(perm) == low_len and int(perm) int(high): continue count += 1 return…Find the numbers that can be expressed as the product of two nonnegative integers insuccession and print them in increasing order. (For example, 30 is such a number as it can bewritten as the product of 5 and 6 (30=5x6), which are two numbers in succession.) The user shouldspecify a maximum value and the program should print all said numbers smaller than or equal tothat value. The program should keep a count of how many numbers were printed and should output that count ,as well as the numbers
- Find the numbers that can be expressed as the product of two nonnegative integers insuccession and print them in increasing order. (For example, 30 is such a number as it can bewritten as the product of 5 and 6 (30=5x6), which are two numbers in succession.) The user shouldspecify a maximum value and the program should print all said numbers smaller than or equal tothat value. The program should keep a count of how many numbers were printed and shouldoutput that count, as well as the numbers. creat a git bash script for the problem abovePerfect numbers are numbers that are equal to the sum of their positive divisors except itself. The smallest perfect number is 6. The positive divisors of 6: The sum of the divisors of 1, 2, 3 and 6 except itself: 1 + 2 + 3 = 6 and 6 is a perfect number. Likewise, the positive divisors of 28: 1, 2, 4, 7, 14, 28 is the sum of the divisors except itself: 1 + 2 + 4 + 7 + 14 = 28 and 28 is a perfect number. So, write a MATLAB function that checks if a given number is a perfect number.Easy Program Please answer fast: you will write a program that calculates the area for ANY regular polygon. Ask the user for the side length of the polygon (the type should be double) and the number of sides (the type should be int). The formula for calculating the area can be seen below and comes in three parts. First, calculate the perimeter of the polygon: given:- perimeter(reg_polygon)=slen*nsides