Question

if ∈(n) represents the number of factors of n hen what is the value of ∈(∈(∈(12)))?

Answer 1

∈(12) = 6
∈(6) = 4
∈(4) = 3

Therefore ∈(∈(∈(12))) = 3

Answer 2

ask me a question if that does not make sense.

Answer 3

distinct or non distinct prime factors, these arithmetic functions are denoted by lower and upper case omega

Answer 4

@Jack17 do you mean prime and composite factors? What do you mean by non-distinct factors here?

Answer 5

oh I thought you meant prime factors, this is called the divisor function denoted by $$d(n)$$

Answer 6

Its 'average' value is $$\ln(n)$$

Answer 7

has the dirichlet series generating function $$\zeta(s)^2=\sum_{n=1}^\infty\frac{d(n)}{n^s}$$

Answer 8

If you know the prime factorization of n, d(n) can be computed easily as follows, $$d(n)=\prod_{p\mid n}(1+v_p(n))$$where $$v_p(n)$$ is the p adic order of n

Answer 9

that's handy

Answer 10

Google divisor function for more information

Answer 11

i am still confused...cant get your answer

Answer 12

its on the first line

Answer 13

i just added alot of information on the divisor function

Answer 14

the factors of twelve are 1,2,3,4,6,12

the number of factors of twelve ∈(12)=6
_____
the factors of six are 1,2,3,6

the number of factors of six ∈(∈(12))=4
_____
...

... ∈(∈(∈(12)))=

Answer 15

listing the divisors is over kill,

Answer 16

if n's prime factorization is $$n=p_1^{a_1}p_2^{a_2}p_3^{a_3}...$$ then the number of divisors of n is
$$(1+a_1)(1+a_2)(1+a_3)..$$

Answer 17

the question dosn't mention prime factors

Answer 18

It doesn't have to, you can calculate the number of divisors of n, with out listing them, if you simply know n's factorization

Answer 19

the question doesn't mention divisors either.

Answer 20

divisors and factors are the same thing

Answer 21

divisors can be negative, factors are usually positive

Answer 22

straight formula

Answer 23

first answer looks good
is there another question here, or just the top one?