Factorization length test?

[LaurV]

Ok. Sorry.

However, your post #3 would look much better without the first sentence. As long as he did not give a definition, neither mine or yours is right or wrong. You should point out that (what you in fact did), but without making assumption of what is right or wrong.

Mea culpa for leveraging on it.

About the second part, well, you WERE looking for someone to fry. Following the discussion related to your teaching method, where you came out a bit empty handed, and I was just in the wrong place at the wrong time with my reply post #2 here. This is my impression, and you can not change it, even if you assume I am paranoid.

Now going seriously, the OP was asking if there is a known method to determine that function. If yes, how efficient it is? It shoud be more complicate then determining the primality of the number. By determining the primality, you can say if the function is 1 or not. Then what? I replied that no such method is available, but by that I understood "except the factoring of the number", which is not very efficient, this just to clarify for you, and avoid further "lessons". Could you give a legitimate answer to that?

[R.D. Silverman]

Originally Posted by LaurV

Ok. Sorry.

However, your post #3 would look much better without the first sentence.

What I said was factually correct. You were grossly wrong. I stated
the facts correctly. You made an assertion about an incorrect definition
when even a superficial reading of the O.P. would make it clear that
NO DEFINITION WAS GIVEN.

As long as he did not give a definition, neither mine or yours is right or wrong.

Wrong again. I actually gave a full definition for F that was consistent with
the values for F that were given by the O.P.

You should point out that (what you in fact did), but without making assumption of what is right or wrong.

This is what I complain about! --> students are too sensitive to being told
that they are wrong! Grow up. I made no "assumption" of right vs. wrong.
I simply stated facts.

About the second part, well, you WERE looking for someone to fry.

False. Stating that a reply to a question is grossly wrong is NOT
"frying someone". And you were "grossly" wrong because of your
assertion about a definition! I will say it again. You made a
claim of an incorrect definition when in fact no definition was given!

The people in this group may not like the way I answer questions.
However, there is one big difference between me and (most of) the
rest of you. I do not shoot my mouth off unless I know what I am
talking about. I answer questions correctly on a consistent basis.
(and yes, I do make mistakes sometimes).

I suggest to you that unless you know what you are talking about, then
you should NOT ANSWER QUESTIONS, especially from novices.

[R.D. Silverman]

Originally Posted by LaurV

But I still would like to get an answer for the question. Is there any word in English math to describe the set of all divisors, except 1 and the number itself?

No.

Before you ask why, I suggest that you think about the following:

For what arithmetic functions would such a concept be useful? (i.e.
all divisors except 1 and the number itself). Call this set of divisors
the Laurv divisors. Do you know anywhere where this set appears?

The definition of 'proper divisor' is useful, because e.g. one can
define a perfect number as the sum of its proper divisors.

[LaurV]

Originally Posted by R.D. Silverman

For what arithmetic functions would such a concept be useful?

Sometimes I really believe that somebody else hacked your account, as one forum member tried to suggest long ago... If you convince me that you are... yourself, then I would make you a list of such functions.

[R.D. Silverman]

Originally Posted by LaurV

Sometimes I really believe that somebody else hacked your account, as one forum member tried to suggest long ago... If you convince me that you are... yourself, then I would make you a list of such functions.

Such a set is not defined in any book or paper of which I am aware.

If you disagree, please give a citation.

Please give your list along with citations.

[R.D. Silverman]

Originally Posted by LaurV

Now going seriously, the OP was asking if there is a known method to determine that function. If yes, how efficient it is?

Allow me to point out that once again you exhibit difficulty in reading.
The O.P. did not ask whether a method was known. He asked
if one existed other than factoring. The answer to that question
is "noone knows". A method can exist without our knowing what it is.

is a well known, well defined function.

Whether there exists a method to compute this function without
factoring n is unknown.

[science_man_88]

Originally Posted by siegert81

Hello,

Is there a specific test for any given integer that determines its number of prime factors?

(Aside from actually finding the actual factors...)

Examples:

F(10) = 2
F(16) = 4
F(17) = 1
F(110) = 3

I see ways of limiting it a bit but it really doesn't give an exact answer: F(x)=y doesn't occur until 2^y so for example I know that F(2^1000+1) has to be less than 1001.