How many factors does a million have?
1 000 000
In number theorem there is a number-theoretic function,Originally Posted by Natasha1
. It is defined as the number of distinct divisors of . For example,
cuz 3 only got 2 factors 1 and 3.
There is a formula, if
is the prime-factorization of
Then,
Thus, since,
Thus,
LetOriginally Posted by srulikbd
Then any factor of is of the form:
where , and each number of this
form is a factor of .
So how many 's are there? Well the first exponent can take
any one of values the second can ....
Hence the number of factors is:
RonL
One more.Originally Posted by srulikbd
This one is more advanced but more elegant
Theorem:
If is a number theoretic function which is multiplicative. Then, the function definied as, is also.
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Note that,
Since, is multiplicative since,
whenever we have that,
is mulitplicative.
Since,
You have,
because or multiplicativity.