Arithmetic function: Difference between revisions

Revision as of 16:39, 12 September 2006

Revision as of 08:41, 20 September 2006

Line 16:

:hence ''c''₄(1)=4.

* ''P''(''n''), the [[Partition function (number theory)|Partition function]] - the number of representations of ''n'' as a sum of positive integers, where we don't distinguish between different orders of the summands. For instance: ''P''(2 · 5) = ''P''(10) = 42 and ''P''(2)''P''(5) = 2 · 7 = 14 ≠≠ 42.

* ππ (''n''), the [[Prime number theorem|Prime counting function]] - the number of [[prime number|primes]] less than or equal to a given number ''n''. We have ππ(1) = 0 and ππ(10) = 4 (the primes below 10 being 2, 3, 5, and 7).

* ωω (''n''), the number of distinct [[prime number|primes]] dividing given number ''n''. We have ωω(1) = 0 and ωω(20) = 2 (the distinct primes dividing 20 being 2 and 5).

* ΛΛ(''n''), the [[von Mangoldt function]] which is defined to be ln(''p'') if ''n'' is an integer power of a prime ''p'' and 0 for all other ''n''.

[[Category:Arithmetic functions|*]]

[[de:Zahlentheoretische Funktion]]

[[he:פונקציה אריתמטית]]

[[hu:Számelméleti függvények]]

[[ko:수론적 함수]]

[[it:Funzione aritmetica]]

[[he:פונקציה אריתמטית]]

[[hu:Számelméleti függvények]]

[[sl:Aritmetična funkcija]]

[[sv:Aritmetisk funktion]]