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In the theory of finite abstract group, abelianness-forcing number $n$ is characterized as a positive integer with standard factorization $n=p_1^{k_1}p_2^{k_2}\cdots p_r^{k_r}$ with $k_i \le 2$ and $... 5answers 94 views Sum Over Solutions to an Equation Two Related Questions Is there any general built-in functionality for computing a sum over solutions to an equation? This is common in number theory. For example, computing sums of the following form.... 1answer 39 views Reverse the reccurence mirrorwise Let be a recurrence for polynomials$R_{m,j}$... 2answers 815 views Determining if a number is divisible by 1000 [closed] I have a number such as: a = 875952; And I want to find if it is divisible by 1000. Is there a concise way of doing that? 0answers 74 views Find the maximum of a function involved with Floor function My function is $$f(H,p) = \left\lfloor \dfrac{\lfloor H/p\rfloor + 3 - \sqrt{(\lfloor H/p\rfloor + 1)^2 - 4H}}{2} \right\rfloor$$ The constraints are$ H \geq p(4p-1) $,$ p $is prime although ... 5answers 419 views Does Mathematica have a twin prime equivalent of PrimePi? Well, it's all there in the title! I'd like to be able to plot the number of twin primes =<x. Is there an inbuilt function that can do this? 1answer 88 views Number-theoretic function using Table I'm trying to make a function to calculate the Log sum of primes over a limited range$1/2n$to$n$or Chebychev theta function over limited range$1/2n$to$n$. This will be used only for even ... 1answer 111 views Where is the Chebyshev function of the second kind in Mathematica/Alpha? I need to perform some computations involving the Chebyshev function of the second kind (sometimes also called the summatory Von Mangoldt function)$\psi(x)$, defined as $$\psi(x) = \sum_{n\le x} \... 2answers 177 views Powers of prime factors of a positive integer n in “Mathematica”? I would like to find the powers of a prime in the unique prime factorization of an n. I want a function f[n,p] such that n,p are given and I need to know what the power of p is. For instance ... 1answer 206 views Is it better to completely forget about the existence of PowersRepresentations? I noticed that in several cases the performance of PowersRepresentations is hugely worse than that of IntegerPartitions. (Mma 10.... 1answer 83 views A function about prime gaps I want to define a f function on Mathematica such as this. f[k] gives the smallest m holds 2k=Prime[m+1]-Prime[m]. For example,$$f=2f=4f=9f=24$$How can i do that?... 2answers 217 views Can Mathematica return the first few terms of a sequence given the first few terms of a Dirichlet Generating Function? For example: a = Sum[1/n^s, {n, 1, 6}]; Expand[a^2] returns a big mess. I want to see something like:$$1/1^s + 2/2^s + 2/3^s + 3/4^s + 2/5^s + 4/6^s + \cdots ... 8answers 2k views Find the minimum integer r such that$(10^r - 1)/37\$ is an integer

I know Element[(10^r - 1)/37, Integers] tests the condition. So what is the command that gives me the minimum integer value r ...
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What is the formula for this numerical series?

I'm developing a questions game. My goal is that the score for each correct answer will increase as the user answers more questions. Initially there are 15 points for each correct answer. Every 4 ...