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/sci/ - Science & Math

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[ERROR] No.3597690 [Reply] [Original]

Given a naural number n, what is number d(n) of possible divisors of that number.

For example 12=2*2*3, so the divisors are 2, 3 and 6, i.e. d(12)=3. Notice that 2*3 doesn't count twice, so it's not just the number of subsets of the prime factors (which would be 2^3).

To keep the notation clear, one might talk about p(n), the number of prime factors, p(n,i), the i-th distince prime factor, and p(n,i,m), the multiplicity of the i-th distince prime factor.

>> No.3597701

("2^3" and "distince" are typos, whatevs)

>> No.3597720

wat? you are talking about one thing then changing it in the next line and it seems you are using the words for other things as what it is used in mathematics.

>> No.3597774

>>3597720
okay, I don't know what the problem with my original post might be, but I describe the function I look for

d(n)=1 if n is prime
d(4)=1 (because 2)
d(6)=1 (because 2,3)
d(8)=1 (because 2)
d(10)=2 (because 2,5)
d(1260)=4 (because 2,3,5,7 (because 1260=2*2*3*3*5*7))

>> No.3597786

ah, maybe you worry about "divisor". well, I don't mean divisor in a fraction but "numbers D I can devide n with such that n/D is an integer"

>> No.3597815

>>3597774
>d(6)=1 (because 2,3)
>d(10)=2 (because 2,5)

Can you elaborate on how these give different d values?

>> No.3597818

number of divisors mean the number of unique numbers that you can divide n with and get a integer, so d(12) = 6 (1,2,3,4,6,12)
so you are looking for the number of unique prime factors of n.

>> No.3597821

>>3597786
Then shouldn't n and 1 be a part of every d(n)? Also
>d(6)=1 (because 2,3)
Shouldn't this say d(6)=2?

>> No.3597825

I have no idea what you are asking or what this post is for.

>d(n)=1 if n is prime
>d(4)=1 (because 2)
>d(6)=1 (because 2,3)
>d(8)=1 (because 2)
>d(10)=2 (because 2,5)
>d(1260)=4 (because 2,3,5,7 (because 1260=2*2*3*3*5*7))

This makes no fucking sense at all. Maybe if you would stop making typos and be clear we could understand you.

Is d(6) equal to 1 (or, like I suppose, 2)?

>> No.3597829

OP: The product over all primes p of ((the number of times p occurs in n)+1).

>> No.3597830

Math fan here,

OP, write the prime factorization of n
See all those exponents?
Add 1 to each one and multiply all those numbers.

Equals d(n). You have to count 1 and n as a divisor for this. If you want to specifically exclude them, just subtract 2 from that answer.

/thread

>> No.3597841

>>3597830
Hey math fan, maybe you should also become a reading comprehension fan.

He's not looking for d(n), fool.

>> No.3597847

you are looking for <span class="math"> \omega (n) [/spoiler]
i dont think there is a way to calculate it but there are approximations such as:

<div class="math"> \omega(n)∼\ln\ln n+B_1+\sum_{k=1}^\infty(-1+\sum_{j=0}^{k-1}(\gamma_j)/(j!))((k-1)!)/((\ln n)^k) </div>
http://mathworld.wolfram.com/DistinctPrimeFactors.html

>> No.3597868

>>3597841
I have made no mistakes. I will let the stupidity of your comment stand on its own.

Next time, be less aggressive and you will have a way to avoid looking like a complete ass.

>> No.3597874

>>3597830
...don't call yourself a math "fan"

math "fan" brings up images of people with flimsy grasps of advanced topics, who think they're ballin cause they aced Calc 1 and learned Pi up to 200 digits because they thought that was the thing for math "fans" to do

>> No.3597883

>>3597874
I don't know who the hell you are, but get the fuck over yourself. Immediately.

>> No.3597903

>>3597868
>>3597883
Fuck off. We don't need your simplistic, copy-paste Wiki-understanding of math here.

>> No.3597918

>>3597868
>I have made no mistakes.
You gave OP a method of calculating d(n), which is not at all what he was looking for. Uh, durr?
See >>3597847 for what this thread is really about. Moron.

>> No.3597925

>>3597903
I am not even sure what purpose you are serving to this thread.

>>3597829
and
>>3597830

both provided a complete correct answer to OP's question, which, as you have apparently chosen to point out, could have been answered by Wikipedia as well.

I'm not sure what else to say to you. If you're really that angry about absolutely nothing, I should suggest psychiatric treatment.

>> No.3597939

>>3597847
>>3597918
OP was in fact looking for d(n) and NOT the number of distinct prime factors of n. If you want to start a thread about a different question, go right ahead.

>> No.3597954

>>3597925
um you're the one who started the whole anger thing off what with accusing someone of being aggressive (when it was really teasing more than aggressive)

and then
> GET THE FUCK OVER YOURSELF - IMMEDIATELY!

>> No.3598000

>>3597954
Whoever "started" it, the fact is that OP asked for a way to calculate d(n) - 2, then proceeded to throw you off by either making a mistake or completely changing the subject and asking a brand new question in a subsequent post. I chose to respond to the first post and gave a correct answer. If you wanted to respond to OP's second post, that's fine by me, but you have no right to attack someone for responding to his first post and disregarding the next.

>> No.3598024

>>3597939
if he wanted d(n) as the number of possible divisors and not number of distinct prime factors then he has been calculating it wrong the intire time in exactly the correct way.

>> No.3598048

>>3598024
>what is number d(n) of possible divisors
>so the divisors are 2, 3 and 6, i.e. d(12)=3

I don't know why you would get that impression from his first post.

>>3597774
This is the first post where he is apparently referring to the number of distinct prime factors, which is a totally new question.

>> No.3598072

>tl dr, OP doesn't even know what the fuck he's asking, /sci/ tries its best to help, but OP's stupid slowly begins to spread

>> No.3598081

>>3598048
d(12)=3? its not, d(12) = 6

>> No.3598104

>>3598081
My best guess was that he was looking for the divisors of 12 excluding 1 and 12 and he forgot to include 4.

d(n) - 2 = 4

If he had been looking for the distinct prime factors, in that post, he probably would have said 2 because I doubt he thinks 6 is prime.

But actually, we will never know.
A new questions arises.
What is the probability that OP was trolling us the whole time?

>> No.3598112

>>3598104
Yeah I meant: d(12) - 2 = 4

>> No.3598134

>>3598112
o, in that case its
<div class="math"> d(n) = \left[\sum_{d|n} 1\right] -2</div>