Arithmetic function: Difference between revisions

Revision as of 01:30, 12 July 2003

Revision as of 18:01, 5 September 2003

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: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.

* π (''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 π(1) = 0 and π(10) = 4 (the primes below 10 being 2, 3, 5, and 7).