- Almost prime
In

number theory , anatural number is called**"k"-almost prime**if and only if it has exactly "k"prime factor s, counted with multiplicity. More formally, a number "n" is "k"-almost prime if and only if Ω("n") = "k", where Ω("n") is the total number of primes in theprime factorization of "n"::$Omega(n)\; :=\; sum\; a\_i\; qquadmbox\{if\}qquad\; n\; =\; prod\; p\_i^\{a\_i\}.$

A natural number is thus prime if and only if it is 1-almost prime, and

semiprime if and only if it is 2-almost prime. The set of "k"-almost primes is usually denoted by "P"_{"k"}. The smallest "k"-almost prime is 2^{"k"}. The first few "k"-almost primes are::

The number π

_{"k"}("n") of positive integers less than or equal to "n" with at most "k" prime divisors (not necessarily distinct) isasymptotic tocite book

last = Tenenbaum

first = Gerald

authorlink = Gerald Tenenbaum

coauthors =

title = Introduction to Analytic and Probabilistic Number Theory

publisher =Cambridge University Press

date = 1995

isbn = 0521412617: $pi\_k(n)\; sim\; left(\; frac\{n\}\{log\; n\}\; ight)\; frac\{(loglog\; n)^\{k-1\{(k\; -\; 1)!\},$a result of Landau. See also the

Hardy–Ramanujan theorem .**References****External links***

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