Number and sum of prime factors of a number

suchith

Given a large number N, do we have any formula to find the number of prime factors and their sum like τ(N) and σ(N) functions?

CONDITION: One should not list the factors of N or is not allowed to factorize N since afterwards it would be just a matter of counting and addition

MrAnchovy

If such a formula ## f(N) ## exists, what would ## f(N) = 1 ## mean?

*uperkurk*

I believe if such a formula does exist then the entire internet would be vulnerable. The internet is secure because of prime number factorisation. See RSA Algorithm

There is a formula to find if a number is prime or not, but not the factors.

${{p_n=1+\displaystyle\sum_{k=1}^{2 \cdot (\lfloor n\ln(n) \rfloor+1)}\left(1-\left\lfloor \frac{1}{n} \cdot \displaystyle\sum_{j=2}^k \left\lceil \frac{3-\displaystyle\sum_{i=1}^j \left\lfloor \frac{\left\lfloor \frac{j}{i} \right\rfloor}{\left\lceil \frac{j}{i} \right\rceil} \right\rfloor}{j} \right\rceil \right\rfloor\right)}$

MrAnchovy

That actually looks like a "formula" to find the ## n ##th prime, but such "formulas" are really just symbolic descriptions of (very ineffecient) algorithms and of no practical importance.

Similar Threads for: Number and sum of prime factors of a number
Thread	Forum	Replies
prove that a rational number squared has each of its prime factors with even exponent	General Math	14
Number Theory least divisor of integer is prime number if integer is not prime	Calculus & Beyond Homework	2
[number theory] find number in certain domain with two prime factorizations	Calculus & Beyond Homework	3
Number of prime factors	Linear & Abstract Algebra	7
Obtaining the number of factors from prime factorization	General Math	3

suchith	Number and sum of prime factors of a number Tweet Given a large number N, do we have any *formula to find the number of prime factors and their sum* like τ(N) and σ(N) functions? CONDITION: One should not list the factors of N or is not allowed to factorize N since afterwards it would be just a matter of counting and addition

MrAnchovy	If such a formula ## f(N) ## exists, what would ## f(N) = 1 ## mean?