# Questions tagged [factoring]

This tag describes challenges related to factoring numbers and polynomials. Not related to the Factor esoteric programming language.

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### Squarefree Palindromes [closed]

Create the shortest function, program, or expression that calculates a sequence of squarefree palindromic numbers. A squarefree number is one which is not evenly divisible by a square number (i.e. ...
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### Fastest way to iterate over sublattice of discrete lattice

I need to construct a functor that iterates over the linear representation of a sub-lattice of size $d_x,d_y,d_z,d_q$ embedded in a lattice of size $n_x,n_y,n_z,n_q$. The sub-lattice corner is ...
186 views

### Find all diagonal counts in only one direction [closed]

If I need to get the number of diagonal squares in all directions: I do the following formula 2 N − 2 − |x − y| − |x + y − N − 1| The above example has 13 and ...
9k views

### Am I not good enough for you?

Background: The current Perfect Numbers challenge is rather flawed and complicated, since it asks you to output in a complex format involving the factors of the number. This is a purely decision-...
917 views

### Generate some rough numbers

Background A number n can be described as B-rough if all of the prime factors of n strictly ...
3k views

### Find the Squarish Root

Write code that when given a positive number $x$ as input, outputs the largest positive divisor of $x$ less than or equal to the square root of $x$. In other words find the largest $n > 0$ ...
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### Prime Factor Encoding

How the encoding works Given a list of bits: Hold a prime (starting with 2) Have a list For each bit in the input If it's the same as the previous bit, add the ...
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### Find the dot product of Rationals

I was at a friend's house for dinner and they suggested the idea of a "Prime-factor vector space". In this space the positive integers are expressed as a vector such that the nth element in the ...
647 views

### Queue Our Decomposition

In this challenge I will ask you to find a QR decomposition of a square matrix. The QR decomposition of matrix A is two Matrices Q and R such that A = QR. In particular we are looking for Q to be an ...
353 views

### Primes ’n’ Digits

This has no practical purpose but it could be fun to golf. Challenge Given a number n, Count the amount of each digit in n and add 1 to each count Take the prime factorization of n Count the amount ...
802 views

### Is my number Unique

In this challenge we learned a way to encode every positive integer using factor trees. Here is how it works: The empty string has value of 1. (S) where ...
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### Determine Superabundance

A superabundant number is an integer n that sets a new upper bound for its ratio with the divisor sum function σ. In other words, n is superabundant if and only if, for all positive integers x ...
382 views

### Encode Factor Trees [duplicate]

I once saw on the xkcd fora a format for expressing numbers in an odd way. In this "factor tree" format: The empty string is 1. Concatenation represents multiplication. A number n enclosed in ...
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### Largest Prime Exponents

Given an integer n >= 2, output the largest exponent in its prime factorization. This is OEIS sequence A051903. Example Let ...
3k views

### Find the sum of the divisors of N

Write a program that displays on the screen the sum of the divisors of a number (1 ≤ N ≤ 100) entered by the user in the range of 1 to N. This is OEIS A000203. Examples: Input: 7 ...
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### Encode an integer

Given positive integer n > 2. We convert it to an array as follows: If it is equal to 2 return an empty array Otherwise ...
537 views

### Number of sums of factors

Given a positive integer n > 1 determine how many numbers can be made by adding integers greater than 1 whose product is n. For example if n = 24 we can express n as a product in the following ways <...
509 views

### Composite Factorization

This is similar to prime factorization, where you find the smallest prime factors of a number (i.e. 8 = 2 x 2 x 2). But this time, you are to return an array/list of the smallest composite factors of ...
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### Calculate the prime factors

We had a prime factorization challenge a while ago, but that challenge is nearly six years old and barely meets our current requirements, so I believe it's time for a new one. Challenge Write a ...
1k views

### Generate n-ary numbers

A secondary number is a positive integer whose prime factors (without multiplicity) are all less than or equal to its square root. 4 is a secondary number, because ...
1k views

### Prime factors buddies

Given an integer N > 1, output all other numbers which prime decompositions have the same digits as the prime decomposition of ...
798 views

### Palindromic Prime Factors

Palindromic prime problems are pretty common, but that's not what this question is about. In this challenge, the number doesn't have to be a palindrome, its prime factors do. Task Your code has to ...
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### Diamond Puzzles!

Explanation: Last year in math class, on homework we would occasionally get these extremely simple, although equally annoying questions called diamond puzzles. These were basically questions where we ...
1k views

### Sums of prime factors

2013 has the prime factorization 3*11*61. 2014 has the prime factorization 2*19*53. An interesting property regarding these ...
1k views

### Novel Prime Factors of Repunits

The Background Folks were talking prime factorization in chat and we found ourselves talking about repunits. Repunits are a subset of the numbers known as repdigits, which are numbers consisting of ...
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### Factoring a 64-bit integer

Write a GOLF assembly program that reads an integer from stdin (followed by a trailing newline), and outputs its prime factors seperated by newlines, followed by a trailing newline on stdout. The ...
7k views

### Check if a number is a product of consecutive integer numbers

Some numbers such as: 6, 12, 20, 30, 42, 56, 60, 90, 120 and so on as can be expressed as a product of consecutive integer numbers as shown below. ...