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Template:Sum of prime factors (with multiplicity)

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The {{sum of prime factors (with multiplicity)}} arithmetic function template returns the sum of prime factors of n (with multiplicity) (sopf(n), integer log of n) of a nonzero integer, otherwise returns an error message.

Usage

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

or

{{sopf|a nonzero integer}}

or

{{integer log|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/A001414/b001414.txt Table of n, integer log of n for n = 1..100000)

Unfortunately, with the transclusion of {{sum of prime factors (with multiplicity)/doc}} via the {{documentation}} template the precious limited nesting levels of templates and/or parser functions were exhausted! :-( Check {{sum of prime factors (with multiplicity)/doc}} directly to see that all the tests are successful. Fortunately, by transcluding {{sum 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
{{sum of prime factors (with multiplicity)|210^2}} 34
{{integer log|210^2}} 34
{{sopf|210^2}} 34
{{sopf|-28}} 11
{{sopf|-5}} 5
{{sopf|1}} 0
{{sopf|7}} 7
{{sopf|15}} 8
{{sopf|27}} 9
{{sopf|30}} 10
{{sopf|111}} 40
{{sopf|5^3 * 11^2}} 37
{{sopf|2^5 * 3^3 * 5}} 24
{{sopf|2^9 * 3^3}} 27
{{sopf|37^2 + 8 * 37^2}} 80
{{sopf|2^9 * (26 + 1)}} 27
{{sopf|89 * 113}} 202
{{sopf|79 * 79}} 158
{{sopf|210^2}} 34
{{sopf|233^2}} 466
{{sopf|10000}} 28
{{sopf|65535}} 282
{{sopf|65536}} 32
{{sopf|65537}} 65537
{{sopf|65539}} 65539
{{sopf|65540}} 151
{{sopf|65541}} 3131
{{sopf|65542}} 32773
{{sopf|65543}} 65543
{{sopf|65547}} 7289
{{sopf|65549}} 171
{{sopf|65551}} 65551
{{sopf|65553}} 21854
{{sopf|65557}} 65557
{{sopf|65559}} 98
{{sopf|65561}} 1290
{{sopf|65563}} 65563
{{sopf|65567}} 552
{{sopf|65569}} 72
{{sopf|65571}} 2001
{{sopf|65573}} 2874
{{sopf|65577}} 21862
{{sopf|65579}} 65579
{{sopf|265535}} 2337
{{sopf|265536}} 479
{{sopf|265537}} 2158
{{sopf|265539}} 88516
{{sopf|265540}} 108
{{sopf|265541}} 265541
{{sopf|265542}} 44262
{{sopf|265543}} 265543
{{sopf|265547}} 265547
{{sopf|265549}} 7214
{{sopf|265551}} 646
{{sopf|265553}} 9186
{{sopf|265557}} 188
{{sopf|265559}} 709
{{sopf|265561}} 265561
{{sopf|265563}} 1578
{{sopf|265567}} 265567
{{sopf|265569}} 88526
{{sopf|265571}} 265571
{{sopf|265573}} 3467
{{sopf|265577}} 703
{{sopf|265579}} 265579
{{sopf|257}} 257
{{sopf|97 * 211}} 308
{{sopf|216 * 211}} 226
{{sopf|1024 * 45}} 31
{{sopf|97 * 257}} 354
{{sopf|3^6 * 5^2}} 28
{{sopf|3 * 5^5}} 28
{{sopf|17^2 * 191}} 225
{{sopf|5 * 7 * 13 * 29}} 54
{{sopf|509^2}} 1018
{{sopf|965535}} 1158
{{sopf|965536}} 245
{{sopf|965537}} 14478
{{sopf|965539}} 11716
{{sopf|965540}} 2131
{{sopf|965541}} 321850
{{sopf|965542}} 25430
{{sopf|965543}} 2904
{{sopf|965547}} 3271
{{sopf|965549}} 304
{{sopf|965551}} 965551
{{sopf|965553}} 321854
{{sopf|965557}} 31178
{{sopf|965559}} 45989
{{sopf|965561}} 679
{{sopf|965563}} 42004
{{sopf|965567}} 965567
{{sopf|965569}} 1511
{{sopf|965571}} 4485
{{sopf|965573}} 787
{{sopf|965577}} 1247
{{sopf|965579}} 5196
{{sopf|1015941}} 4715
{{sopf|997 * 1019}} 2016
{{sopf|1015943}} 2016
{{sopf|1015945}} 29039
{{sopf|1015947}} 882
{{sopf|1015949}} 4891
{{sopf|1015950}} 549

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

Code Result
{{sopf|0}} Expression error: Unrecognized word "strong".
{{sopf|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 = * }} }}</includeonly>

See also







External links