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# Template:Dedekind psi

The following documentation is located at Template:Dedekind psi/doc.

The {{Dedekind psi}} arithmetic function template returns the Dedekind psi function of ${\displaystyle \scriptstyle n\,}$ (${\displaystyle \scriptstyle \psi (n)\,}$) of a nonzero integer, otherwise returns an error message.

## Usage

{{Dedekind psi|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/A001615/b001615.txt Table of n, psi(n) for n = 1..10000)

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

Code Result
{{Dedekind psi|210^2}} 120960
{{Dedekind psi|210^2}} 120960
{{Dedekind psi|-28}} 48
{{Dedekind psi|-5}} 6
{{Dedekind psi|1}} 1
{{Dedekind psi|7}} 8
{{Dedekind psi|15}} 24
{{Dedekind psi|27}} 36
{{Dedekind psi|30}} 72
{{Dedekind psi|111}} 152
{{Dedekind psi|5^3 * 11^2}} 19800
{{Dedekind psi|2^5 * 3^3 * 5}} 10368
{{Dedekind psi|2^9 * 3^3}} 27648
{{Dedekind psi|37^2 + 8 * 37^2}} 16872
{{Dedekind psi|2^9 * (26 + 1)}} 27648
{{Dedekind psi|89 * 113}} 10260
{{Dedekind psi|79 * 79}} 6320
{{Dedekind psi|210^2}} 120960
{{Dedekind psi|233^2}} 54522
{{Dedekind psi|10000}} 18000
{{Dedekind psi|65535}} 111456
{{Dedekind psi|65536}} 98304
{{Dedekind psi|65537}} 65538
{{Dedekind psi|65539}} 65540
{{Dedekind psi|65540}} 123120
{{Dedekind psi|65541}} 99904
{{Dedekind psi|65542}} 98316
{{Dedekind psi|65543}} 65544
{{Dedekind psi|65547}} 87408
{{Dedekind psi|65549}} 73440
{{Dedekind psi|65551}} 65552
{{Dedekind psi|65553}} 87408
{{Dedekind psi|65557}} 65558
{{Dedekind psi|65559}} 96432
{{Dedekind psi|65561}} 66852
{{Dedekind psi|65563}} 65564
{{Dedekind psi|65567}} 66120
{{Dedekind psi|65569}} 86400
{{Dedekind psi|65571}} 95424
{{Dedekind psi|65573}} 68448
{{Dedekind psi|65577}} 87440
{{Dedekind psi|65579}} 65580
{{Dedekind psi|265535}} 332640
{{Dedekind psi|265536}} 532224
{{Dedekind psi|265537}} 267696
{{Dedekind psi|265539}} 354056
{{Dedekind psi|265540}} 559872
{{Dedekind psi|265541}} 265542
{{Dedekind psi|265542}} 531096
{{Dedekind psi|265543}} 265544
{{Dedekind psi|265547}} 265548
{{Dedekind psi|265549}} 272764
{{Dedekind psi|265551}} 416640
{{Dedekind psi|265553}} 274740
{{Dedekind psi|265557}} 387072
{{Dedekind psi|265559}} 309120
{{Dedekind psi|265561}} 265562
{{Dedekind psi|265563}} 372960
{{Dedekind psi|265567}} 265568
{{Dedekind psi|265569}} 354096
{{Dedekind psi|265571}} 265572
{{Dedekind psi|265573}} 331200
{{Dedekind psi|265577}} 295680
{{Dedekind psi|265579}} 265580
{{Dedekind psi|257}} 258
{{Dedekind psi|97 * 211}} 20776
{{Dedekind psi|216 * 211}} 91584
{{Dedekind psi|1024 * 45}} 110592
{{Dedekind psi|97 * 257}} 25284
{{Dedekind psi|3^6 * 5^2}} 29160
{{Dedekind psi|3 * 5^5}} 15000
{{Dedekind psi|17^2 * 191}} 58752
{{Dedekind psi|5 * 7 * 13 * 29}} 20160
{{Dedekind psi|509^2}} 259590
{{Dedekind psi|965535}} 1572480
{{Dedekind psi|965536}} 1709568
{{Dedekind psi|965537}} 980016
{{Dedekind psi|965539}} 977256
{{Dedekind psi|965540}} 1814400
{{Dedekind psi|965541}} 1287392
{{Dedekind psi|965542}} 1524600
{{Dedekind psi|965543}} 968448
{{Dedekind psi|965547}} 1404864
{{Dedekind psi|965549}} 1105272
{{Dedekind psi|965551}} 965552
{{Dedekind psi|965553}} 1287408
{{Dedekind psi|965557}} 996736
{{Dedekind psi|965559}} 1471360
{{Dedekind psi|965561}} 1029600
{{Dedekind psi|965563}} 1007568
{{Dedekind psi|965567}} 965568
{{Dedekind psi|965569}} 1071360
{{Dedekind psi|965571}} 1305360
{{Dedekind psi|965573}} 1109760
{{Dedekind psi|965577}} 1292416
{{Dedekind psi|965579}} 970776
{{Dedekind psi|1015941}} 1373440
{{Dedekind psi|997 * 1019}} 1017960
{{Dedekind psi|1015943}} 1017960
{{Dedekind psi|1015945}} 1393344
{{Dedekind psi|1015947}} 1365120
{{Dedekind psi|1015949}} 1166880
{{Dedekind psi|1015950}} 2630880

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

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

## Code


<noinclude><!-- {{documentation}} --><!-- We can't use it here, we reached the nesting levels limit of templates and/or parser functions!

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: ( abs ({{{1|1}}}) ) * (1 + 0{{mpf| {{{1|1}}} |sep = ) * (1 + |key/val_sep = ^(-1) * 1^}} ) }}</includeonly>