Consider the following integer n= 4806841016250 = 2^1 * 3^6 * 5^4 * 7^4 * 13^3...
Consider the following integer
n= 4806841016250 = 2^1 * 3^6 * 5^4 * 7^4 * 13^3
a) How many positive divisors does n have?
b) How many of the positive divisors of n are perfect cubes? That
is, the number can be written as (k)^3 for some k∈Z
c) How many of the positive divisors of n are relatively prime with
6?
Homework Answers
Add Answer to:
Consider the following
integer
n= 4806841016250 = 2^1 * 3^6 * 5^4 * 7^4 * 13^3...
Problem 5. (1 point) [5 Marks] Consider the following integer n = 516734400 = 2 ·...
Problem 5. (1 point) [5 Marks] Consider the following integer n = 516734400 = 2 · 37 · 52 · 72 · 133. a) How many positive divisors does n have? b) How many of the positive divisors of n are perfect cubes? That is, the number can be written as (k)3 for some k e Z. c) How many of the positive divisors of n are relatively prime with 21? A. I am finished this question
Prime numbers are the building blocks of all integers greater than 1. Any integer n >...
Prime numbers are the building blocks of all integers greater than 1. Any integer n > 1 can be written as a unique product of primes i.e. n = p1 × p2 × ... × pm. Here, pi are primes such that p1 ≤ p2 ≤ ... ≤ pm. Take, for example, the number 18. It can be written as 18 = 2 × 3 × 3. 1. Write a Python function prime divisors(n) which accept an integer n and...
Challenge activity: A partition of a positive integer n is the expression of n as the sum of positive integers, whe...
Challenge activity: A partition of a positive integer n is the expression of n as the sum of positive integers, where order does not matter. For example, two partitions of 7 are 7 1+1+1+4 and 7=1+1+1+2+2. A partition of n is perfect if every integer from 1 to n can be written uniquely as the sum of elements in the partition. 1+1+1+4 is perfect since 1-7 are expressed only as 1, 1+1, 1+1+1, 4, 1+4, 1+1+4 and 1+1+1+4, but 1+1+1+2+2...
DEFINITION: For a positive integer n, τ(n) is the number of positive divisors of n and...
DEFINITION: For a positive integer n, τ(n) is the number of
positive divisors of n and σ(n) is the sum of those divisors.
4. The goal of this problem is to prove the inequality in part (b), that o(1)+(2)+...+on) < nº for each positive integer n. The first part is a stepping-stone for that. (a) (10 points.) Fix positive integers n and k with 1 <ksn. (i) For which integers i with 1 <i<n is k a term in the...
IN PYHTON CODE Question #3 Produce a function prime_factors.dict that has one integer variable n that...
IN PYHTON CODE
Question #3 Produce a function prime_factors.dict that has one integer variable n that is assumed to be greater than 1. The function will return a dictionary with keys the integers from 2 to n, inclusive, and with values the set of prime factors of each key. So, the command prime_factors.dict (8) will return the dictionary 2 123,3: 3),4 2),5 (53,6 2,3),7:7),8 {2)) Note that even though the prime number 2 appears twice in the prime fac- torization...
A perfect number is a positive integer that is equal to the sum of its (proper)...
A perfect number is a positive integer that is equal to the sum of its (proper) positive divisors, including 1 but excluding itself. A divisor of a number is one which divides the number evenly (i.e., without a remainder). For example, consider number 6. Its divisors are 1, 2, 3, and 6. Since we do not include number itself, we only have 1, 2, and 3. Because the sum of these divisors of 6 is 6, i.e., 1 + 2...
A positive integer greater than 1 is said to be prime if it has no divisors...
A positive integer greater than 1 is said to be prime if it has no divisors other than 1 and itself. A positive integer greater than 1 is composite if it is not prime. Write a program that defines two functions is_prime() and list_primes(). is_prime() will determine if a number is prime. list_primes() will list all the prime numbers below itself other than 1. For example, the first five prime numbers are: 2, 3, 5, 7 and 11." THE PROGRAM...
Please paste your code and a screenshot of your output! 1. An integer n is divisible...
Please paste your code and a screenshot of your output!
1. An integer n is divisible by 9 if the sum of its digits is divisible by 9. Develop a program to determine whether or not the following numbers are divisible by 9: n= 154368 n 621594 n-123456 2. A number is said to be perfect if the sum of its divisors (except for itself) is equal to itself. For example, 6 is a perfect number because the sum of...
A perfect number is a positive integer that equals the sum of all of its divisors...
A perfect number is a positive integer that equals the sum of all of its divisors (including the divisor 1 but excluding the number itself). For example 6, 28 and 496 are perfect numbers because 6=1+2+3 28 1 + 2 + 4 + 7 + 14 496 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 Write a program to read a positive integer value, N, and find the smallest perfect number...
A prime number is a positive integer whose positive integer divisors are 1 and the number....
A prime number is a positive integer whose positive integer divisors are 1 and the number. E.g. 17 is a prime number -23 is a not prime number 28 is not a prime number -45 is not a prime number The only even prime number is 2 Write a boolean function, isPrime that return true if its integer parameter is a prime and false if its integer parameter is not a prime number. A simple prime number algorithm is if...
Problem 5. (1 point) [5 Marks] Consider the following integer n = 516734400 = 2 · 37 · 52 · 72 · 133. a) How many positive divisors does n have? b) How many of the positive divisors of n are perfect cubes? That is, the number can be written as (k)3 for some k e Z. c) How many of the positive divisors of n are relatively prime with 21? A. I am finished this question
Challenge activity: A partition of a positive integer n is the expression of n as the sum of positive integers, where order does not matter. For example, two partitions of 7 are 7 1+1+1+4 and 7=1+1+1+2+2. A partition of n is perfect if every integer from 1 to n can be written uniquely as the sum of elements in the partition. 1+1+1+4 is perfect since 1-7 are expressed only as 1, 1+1, 1+1+1, 4, 1+4, 1+1+4 and 1+1+1+4, but 1+1+1+2+2...
DEFINITION: For a positive integer n, τ(n) is the number of
positive divisors of n and σ(n) is the sum of those divisors.
4. The goal of this problem is to prove the inequality in part (b), that o(1)+(2)+...+on) < nº for each positive integer n. The first part is a stepping-stone for that. (a) (10 points.) Fix positive integers n and k with 1 <ksn. (i) For which integers i with 1 <i<n is k a term in the...
IN PYHTON CODE
Question #3 Produce a function prime_factors.dict that has one integer variable n that is assumed to be greater than 1. The function will return a dictionary with keys the integers from 2 to n, inclusive, and with values the set of prime factors of each key. So, the command prime_factors.dict (8) will return the dictionary 2 123,3: 3),4 2),5 (53,6 2,3),7:7),8 {2)) Note that even though the prime number 2 appears twice in the prime fac- torization...
Please paste your code and a screenshot of your output!
1. An integer n is divisible by 9 if the sum of its digits is divisible by 9. Develop a program to determine whether or not the following numbers are divisible by 9: n= 154368 n 621594 n-123456 2. A number is said to be perfect if the sum of its divisors (except for itself) is equal to itself. For example, 6 is a perfect number because the sum of...
A perfect number is a positive integer that equals the sum of all of its divisors (including the divisor 1 but excluding the number itself). For example 6, 28 and 496 are perfect numbers because 6=1+2+3 28 1 + 2 + 4 + 7 + 14 496 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 Write a program to read a positive integer value, N, and find the smallest perfect number...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago