# Tagged Questions

Questions on the number-theoretic functionality of Mathematica.

3answers
116 views

### Can you compute more terms in this sequence?

I am trying to identify a sequence related to the von Mangoldt function matrix. Since I believe/conjecture that the columns in the matrix have period lengths as in this sequence b: ...
0answers
75 views

### Solution of a set of quadratic congruences (Chinese remainder)

Edit: Please remove this question. I think there are mathematics error in what I am asking. You are welcome to edit the question if you can state the problem correctly. I have a set of quadratic ...
1answer
76 views

### One of the factors greater than $x$ [closed]

Is there an easy way to tell Mathematica to find one of the prime factors of $n$ greater than $x$. For example, if $n=1299709\cdot 7919 \cdot 17$, is there a way to request a factor greater than ...
4answers
840 views

### Integers which are the sum of both two and three consecutive squares

This is a math problem I came across the other day: I would like to know what would be a good way (esp. performance-wise) to check all first, lets say, 1000000, natural numbers if they can be ...
1answer
118 views

### Mathematica spitting code back when using Resolve over a large range of interest

I've just started using Mathematica and have encountered my first issue. Below are two commands which only differ in the range of values I am asking Mathematica to check. The first works fine, but the ...
2answers
193 views

### A problem about fixed point iteration theory

Description Recently, I have been learning a couse called "Numerical Analysis". The fixed point iteration theory was introducted to solve the ...
2answers
174 views

### Approximation to the prime counting function

Is there a function similar to PrimePi that gives approximate value for large numbers? In particular, I need a reasonably good approximation for $\pi(x)$, where ...
2answers
377 views

### Counting the zeros in a factorial expansion [closed]

A number, as big as 1000! (! = factorial) is given. I need to find how many zeros are there in the number. I counted the no of terminal zeros by dividing 5, 25, 125, ... (untill fifth power < ...
1answer
38 views

### Q-Multinomial Coefficient [closed]

How can one compute the q-Multinomial Coefficient as a function of q,m and a list {n1,n2,n3,...} in Mathematica? See http://mathworld.wolfram.com/q-MultinomialCoefficient.html for the definition.
5answers
256 views

### Triangular numbers boolean function

I read the new book by Paul Wellin Programming in Mathematica. There is an exercise about triangular numbers. (The n-th triangular number is defined as the sum of ...
1answer
285 views

### the more effective method to find 21 digits armstrong number

In recreational number theory, a narcissistic number (also known as a pluperfect digital invariant (PPDI), an Armstrong number(after Michael F. Armstrong) or a plus perfect number) is a number that is ...
5answers
242 views

### Write a number as the product of its two largest divisors

For even n >= 10 && n <= 98 I want to write n as the product of its two largest divisors (excluding ...
5answers
787 views

### A question regarding 1 divided 243

Here is a problem due to Feynman. If you take 1 divided by 243 you get 0.004115226337 .... It goes a little cockeyed after 559 when you're carrying out the decimal expansion, but it soon straightens ...
5answers
741 views

### Write any positive integer as a sum of squares

With n = 17 I would like to get {4, 1} and with n = 999 {31, 6, 1, 1} so that, for example, ...
1answer
93 views

3answers
269 views

### Find integer values of p such that $(2^p - (2^2)(3^2))/ (3^3)$ is an integer

Find integer values of p such that $(2^p - (2^2)(3^2))/ (3^3)$ is an integer.
0answers
85 views

### Simplifying expressions involving Divisible

FullSimplify[ Divisible[p^2 - 1, 24] , Element[p, Primes] && p > 3] Should evaluate to True, but I get ...
1answer
264 views

### random number visualization without generator (Spectral Test)

Does anyone have codes for using only numbers to make this kind of random-number visualization and not requiring a number generator? ...
2answers
397 views

### Next highly composite number?

R language has this function 'nextn' (link) which computes the next highly composite number greater than a given one, which is used to find the optimal padding size for the subsequent FFT operation. ...
1answer
193 views

### Expressing large numbers in index form

I have a quick question. Is there anyway of expressing a large number as a power of another number in Mathematica? By this, I mean for example, $1237940039285380274899124224 = 512^{10}$. Is there a ...
1answer
148 views

### How can I program the RiemannR function using the LogIntegral command?

I would like to program the RiemannR function using the LogIntegral command because I would like to later experiment with a ...
1answer
179 views

### Hermite Normal Form in “columns” convention

After describing the Hermite Normal Form (HNF), MathWorld explains: The Hermite normal form for integer matrices is implemented in Mathematica as ...
1answer
524 views

### Function to Determine Lucky Numbers

Given a list of the form {1, 3, 5, 7, ...}, the lucky numbers are obtained by looking at the first list element after 1 (so 3 in this case), and deleting all list ...
1answer
178 views

### Finding the largest integer that cannot be partitioned in a certain way

I want to use Mathematica to solve the problem: Find the maximum $k$ such that $6x+9y+20z=k$ does not have a non-negative solution. I tried FrobeniusSolve. ...
1answer
321 views

### How does Mathematica calculate the nth prime?

When I enter Prime[2000000000000], the two-trillionth prime, Mathematica gives 61427839512211 for the answer after several ...
1answer
183 views

### Generating a list of all factorizations

What is the best way to generate a list of all factorizations of some number $n$? I'm quite new to Mathematica so this might be obvious. I have been trying some basic stuff with ...
3answers
200 views

### Why do these two different zetas produce the same value?

Zeta[-13] == Zeta[-1] == -1/12 Why do these two different zetas produce the same value?
1answer
135 views

### Another MoebiusMu question

When I evaluate the Mertens function to infinity: NSum[MoebiusMu[k], {k, 1, \[Infinity]}] I get -1, but I expected to get -2. I wanted to modify the ...
3answers
533 views

### Implementing the Farey sequence efficiently

There is of course the silly implementation: FareySequence[n_] := Union[Flatten[Table[j/i, {i, 1, n}, {j, 0, i}]]] However, there are numerous properties and ...
1answer
333 views

### What is the confidence limit on this convergence?

When I run this, Product[n^MoebiusMu[n],{n,1,Infinity}] I get $\frac{1}{4 \pi^{2}}$ Over on Math Overflow they are saying it shouldn't happen. So, how do ...
3answers
227 views

### How could I implement the equivalent of NextPrime

I would like to know what an implementation of the function NextPrime would look like if it were implemented in Mathematica's core language.