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Template:Number of prime factors (with multiplicity)

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The {{number of prime factors (with multiplicity)}} arithmetic function template returns Omega(n), number of prime factors of n (with multiplicity) (big Omega(n)) of a nonzero integer, otherwise returns an error message.

Usage

{{number of prime factors (with multiplicity)|a nonzero integer}}

or

{{big Omega|a nonzero integer}}

Valid input

A nonzero integer less than 1031 2 = 1062961 (validation is done by the {{mpf}} arithmetic function template).

Examples

Examples with valid input (check with https://oeis.org/A001222/b001222.txt Table of n, Omega(n) for n = 1..100000)

Unfortunately, with the transclusion of {{Number of prime factors (with multiplicity)/doc}} via the {{documentation}} template the precious limited nesting levels of templates and/or parser functions were exhausted! :-( Check {{Number of prime factors (with multiplicity)/doc}} directly to see that all the tests are successful. Fortunately, by transcluding {{Number of prime factors (with multiplicity)/doc}} directly, borrowing the minimum code needed here from the {{documentation}} template, we manage to not exhaust the limit! :-)

Code Result
{{number of prime factors (with multiplicity)|210^2}} 8
{{big Omega|210^2}} 8
{{big Omega|-28}} 3
{{big Omega|-5}} 1
{{big Omega|1}} 0
{{big Omega|7}} 1
{{big Omega|15}} 2
{{big Omega|27}} 3
{{big Omega|30}} 3
{{big Omega|111}} 2
{{big Omega|5^3 * 11^2}} 5
{{big Omega|2^5 * 3^3 * 5}} 9
{{big Omega|2^9 * 3^3}} 12
{{big Omega|37^2 + 8 * 37^2}} 4
{{big Omega|2^9 * (26 + 1)}} 12
{{big Omega|89 * 113}} 2
{{big Omega|79 * 79}} 2
{{big Omega|210^2}} 8
{{big Omega|233^2}} 2
{{big Omega|10000}} 8
{{big Omega|65535}} 4
{{big Omega|65536}} 16
{{big Omega|65537}} 1
{{big Omega|65539}} 1
{{big Omega|65540}} 5
{{big Omega|65541}} 3
{{big Omega|65542}} 2
{{big Omega|65543}} 1
{{big Omega|65547}} 3
{{big Omega|65549}} 3
{{big Omega|65551}} 1
{{big Omega|65553}} 2
{{big Omega|65557}} 1
{{big Omega|65559}} 4
{{big Omega|65561}} 2
{{big Omega|65563}} 1
{{big Omega|65567}} 2
{{big Omega|65569}} 4
{{big Omega|65571}} 3
{{big Omega|65573}} 2
{{big Omega|65577}} 2
{{big Omega|65579}} 1
{{big Omega|265535}} 3
{{big Omega|265536}} 9
{{big Omega|265537}} 2
{{big Omega|265539}} 2
{{big Omega|265540}} 6
{{big Omega|265541}} 1
{{big Omega|265542}} 3
{{big Omega|265543}} 1
{{big Omega|265547}} 1
{{big Omega|265549}} 2
{{big Omega|265551}} 4
{{big Omega|265553}} 2
{{big Omega|265557}} 4
{{big Omega|265559}} 3
{{big Omega|265561}} 1
{{big Omega|265563}} 4
{{big Omega|265567}} 1
{{big Omega|265569}} 2
{{big Omega|265571}} 1
{{big Omega|265573}} 3
{{big Omega|265577}} 3
{{big Omega|265579}} 1
{{big Omega|257}} 1
{{big Omega|97 * 211}} 2
{{big Omega|216 * 211}} 7
{{big Omega|1024 * 45}} 13
{{big Omega|97 * 257}} 2
{{big Omega|3^6 * 5^2}} 8
{{big Omega|3 * 5^5}} 6
{{big Omega|17^2 * 191}} 3
{{big Omega|5 * 7 * 13 * 29}} 4
{{big Omega|509^2}} 2
{{big Omega|965535}} 4
{{big Omega|965536}} 8
{{big Omega|965537}} 2
{{big Omega|965539}} 2
{{big Omega|965540}} 5
{{big Omega|965541}} 2
{{big Omega|965542}} 3
{{big Omega|965543}} 2
{{big Omega|965547}} 5
{{big Omega|965549}} 4
{{big Omega|965551}} 1
{{big Omega|965553}} 2
{{big Omega|965557}} 2
{{big Omega|965559}} 3
{{big Omega|965561}} 3
{{big Omega|965563}} 2
{{big Omega|965567}} 1
{{big Omega|965569}} 3
{{big Omega|965571}} 3
{{big Omega|965573}} 3
{{big Omega|965577}} 3
{{big Omega|965579}} 2
{{big Omega|997 * 1019}} 2
{{big Omega|1015943}} 2

Examples with invalid input (argument validation by {{big Omega}} is omitted to spare some precious limited nesting levels of templates and/or parser functions).

Code Result
{{big Omega|0}} Expression error: Unrecognized word "strong".
{{big Omega|1031^2}} Expression error: Unrecognized word "strong".

Code

<noinclude><!-- {{documentation}} --><!-- We can't use it here, the precious limited nesting levels of templates and/or parser functions get exhausted! 

So we just borrow the necessary code from it instead.

--><div style="text-align: center; font-size: smaller;">The following [[Help:Documenting templates|documentation]] is located at [[Template:{{PAGENAME}}/doc]].</div>{{Template:{{PAGENAME}}/doc}}<!--

--></noinclude><includeonly>{{#expr: 0{{mpf| {{{1|1}}} |sep = + |key/val_sep = ^0 * }} }}</includeonly>

See also