23. A perfect number is a positive integer that is equal to the sum of its positive divisorsexcept the number itself. The first two perfect numbers are 6 and 28 since 6=1+2+3and 28=1+2+4+7+14. Write a computer program that finds thefirst four perfect numbers
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23. A perfect number is a positive integer that is equal to the sum of its positive divisors
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
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) -> 12Perfect 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.Three numbersa. Write a program that reads three numbers and prints “all the same” if they are allthe same, “all different” if they are all different, and “neither” otherwise.b. Write a program that reads three numbers and prints “increasing” if they are inincreasing order, “decreasing” if they are in decreasing order, and “neither”otherwise. Here, “increasing” means “strictly increasing”, with each value largerthan its predecessor. The sequence 3 4 4 would not be considered increasing.c. Repeat part b. but before reading the numbers, ask the user whetherincreasing/decreasing should be “strict” or “lenient”. In lenient mode, thesequence 3 4 4 is increasing and the sequence 4 4 4 is both increasing anddecreasing
- Perfect numbers are numbers that equal the sum of their positive divisors except itself. The smallest perfect number is 6. 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 C program that checks if a given number is a perfect number.Knight's Tour: The Knight's Tour is a mathematical problem involving a knight on a chessboard. The knight is placed on the empty board and, moving according to the rules of chess, must visit each square exactly once. There are several billion solutions to the problem, of which about 122,000,000 have the knight finishing on the same square on which it begins. When this occurs the tour is said to be closed. Your assignment is to write a program that gives a solution to the Knight's Tour problem recursively. You must hand in a solution in C++ AND Java. The name of the C++ file should be "main.cc" and the name of the Java file should be "Main.java". Write C++ only with a file name of main.cc Please run in IDE and check to ensure that there are no errors occuring Output should look similar to: 1 34 3 18 49 32 13 16 4 19 56 33 14 17 50 31 57 2 35 48 55 52 15 12 20 5 60 53 36 47 30 51 41 58 37 46 61 54 11 26 6 21 42 59 38 27 64 29 43 40 23 8 45 62 25 10 22 7 44 39 24 9 28 63An 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.
- 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.Q1: Write a program that reads a set of N integers. Then, the program finds and outputs the sum of the even values and the sum of the odd values of them. For example: if the value entered for N=5, and the five integers are 3, 6, 2, 9, 7. Then the sum of even values (6+2 = 8), and the sum of odd values (3+9+7 = 19) Q2: Write a program that reads some numbers until it reaches a specific value (assume -1 is a stop value in this case). The program should find and outputs the average of all of the numbers (between 10...40) except the stop value (-1). For example: If the numbers look like: 12 5 30 48 -1. Then, the average of the numbers: (12+30)/2 = 21.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 Descrintion
- 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 numbersFind 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 abovePart a:Finding Pythagorean Triples with OpenMPWrite a program that calculates Pythagorean triples using nested for loops. The Pythagorean Theorem states the following:?2 + ?2 = ?2Where a, b, and c are whole numbers. Part b: Modifying the Pythagorean Theorem Modify the Pythagorean Theorem by either adding or subtracting a times b on the left-hand-side, and run the program again. Are there integer solutions for this??2 + ?2 + ??= ?2