Additive function: Difference between revisions

Revision as of 23:55, 1 January 2025

Latest revision as of 01:40, 2 February 2025

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* The restriction of the [[Logarithm|logarithmic function]] to <math>\N.</math>

* The '''multiplicity''' of a [[Prime number|prime]] factor ''p'' in ''n'', that is the largest exponent ''m'' for which ''p^m'' [[Divisor|divides]] ''n''. {{anchor|Integer logarithim}}

* {{anchor|Integer logarithm}} ''a''₀(''n'') – the sum of primes dividing ''n'' counting multiplicity, sometimes called sopfr(''n''), the potency of ''n'' or the '''integer logarithm''' of ''n'' {{OEIS|A001414}}. For example:

::''a''₀(4) = 2 + 2 = 4

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::Ω(2002) = 4

::Ω(2003) = 1

::Ω(54,032,858,972,279) = Ω(11 ⋅ 1993² ⋅ 1236661) = 4  ;

::Ω(54,032,858,972,302) = Ω(2 ⋅ 7² ⋅ 149 ⋅ 2081 ⋅ 1778171) = 6

::Ω(20,802,650,704,327,415) = Ω(5 ⋅ 7 ⋅ 11² ⋅ 1993² ⋅ 1236661) = 7.