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Template:Sum of distinct prime factors
The {{sum of distinct prime factors}} arithmetic function template returns the sum of distinct prime factors of n (sodpf(n)) of a nonzero integer, otherwise returns an error message.
Usage
- {{sum of distinct prime factors|a nonzero integer}}
or
- {{sodpf|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/A008472/b008472.txt Table of n, sodpf(n) for n = 1..100000)
Unfortunately, with the transclusion of {{sum of distinct prime factors/doc}} via the {{documentation}} template the precious limited nesting levels of templates and/or parser functions were exhausted! :-( Check {{sum of distinct prime factors/doc}} directly to see that all the tests are successful. Fortunately, by transcluding {{sum of distinct prime factors/doc}} directly, borrowing the minimum code needed here from the {{documentation}} template, we manage to not exhaust the limit! :-)
Code Result {{sum of distinct prime factors|210^2}} 17 {{sodpf|210^2}} 17 {{sodpf|-28}} 9 {{sodpf|-5}} 5 {{sodpf|1}} 0 {{sodpf|7}} 7 {{sodpf|15}} 8 {{sodpf|27}} 3 {{sodpf|30}} 10 {{sodpf|111}} 40 {{sodpf|5^3 * 11^2}} 16 {{sodpf|2^5 * 3^3 * 5}} 10 {{sodpf|2^9 * 3^3}} 5 {{sodpf|37^2 + 8 * 37^2}} 40 {{sodpf|2^9 * (26 + 1)}} 5 {{sodpf|89 * 113}} 202 {{sodpf|79 * 79}} 79 {{sodpf|210^2}} 17 {{sodpf|233^2}} 233 {{sodpf|10000}} 7 {{sodpf|65535}} 282 {{sodpf|65536}} 2 {{sodpf|65537}} 65537 {{sodpf|65539}} 65539 {{sodpf|65540}} 149 {{sodpf|65541}} 3131 {{sodpf|65542}} 32773 {{sodpf|65543}} 65543 {{sodpf|65547}} 7286 {{sodpf|65549}} 171 {{sodpf|65551}} 65551 {{sodpf|65553}} 21854 {{sodpf|65557}} 65557 {{sodpf|65559}} 57 {{sodpf|65561}} 1290 {{sodpf|65563}} 65563 {{sodpf|65567}} 552 {{sodpf|65569}} 72 {{sodpf|65571}} 2001 {{sodpf|65573}} 2874 {{sodpf|65577}} 21862 {{sodpf|65579}} 65579 {{sodpf|265535}} 2337 {{sodpf|265536}} 466 {{sodpf|265537}} 2158 {{sodpf|265539}} 88516 {{sodpf|265540}} 106 {{sodpf|265541}} 265541 {{sodpf|265542}} 44262 {{sodpf|265543}} 265543 {{sodpf|265547}} 265547 {{sodpf|265549}} 7214 {{sodpf|265551}} 646 {{sodpf|265553}} 9186 {{sodpf|265557}} 188 {{sodpf|265559}} 709 {{sodpf|265561}} 265561 {{sodpf|265563}} 1575 {{sodpf|265567}} 265567 {{sodpf|265569}} 88526 {{sodpf|265571}} 265571 {{sodpf|265573}} 3467 {{sodpf|265577}} 703 {{sodpf|265579}} 265579 {{sodpf|257}} 257 {{sodpf|97 * 211}} 308 {{sodpf|216 * 211}} 216 {{sodpf|1024 * 45}} 10 {{sodpf|97 * 257}} 354 {{sodpf|3^6 * 5^2}} 8 {{sodpf|3 * 5^5}} 8 {{sodpf|17^2 * 191}} 208 {{sodpf|5 * 7 * 13 * 29}} 54 {{sodpf|509^2}} 509 {{sodpf|965535}} 1158 {{sodpf|965536}} 237 {{sodpf|965537}} 14478 {{sodpf|965539}} 11716 {{sodpf|965540}} 2129 {{sodpf|965541}} 321850 {{sodpf|965542}} 25430 {{sodpf|965543}} 2904 {{sodpf|965547}} 3265 {{sodpf|965549}} 287 {{sodpf|965551}} 965551 {{sodpf|965553}} 321854 {{sodpf|965557}} 31178 {{sodpf|965559}} 45989 {{sodpf|965561}} 679 {{sodpf|965563}} 42004 {{sodpf|965567}} 965567 {{sodpf|965569}} 1511 {{sodpf|965571}} 4485 {{sodpf|965573}} 787 {{sodpf|965577}} 1247 {{sodpf|965579}} 5196 {{sodpf|1015941}} 4715 {{sodpf|997 * 1019}} 2016 {{sodpf|1015943}} 2016 {{sodpf|1015945}} 29039 {{sodpf|1015947}} 879 {{sodpf|1015949}} 4891 {{sodpf|1015950}} 544
Examples with invalid input (argument validation by {{sodpf}} is omitted to spare some precious limited nesting levels of templates and/or parser functions).
Code Result {{sodpf|0}} Expression error: Unrecognized word "strong". {{sodpf|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 = * 1^}} }}</includeonly>
See also
- {{distinct prime factors up to sqrt(n)}} or {{dpf le sqrt(n)}}
- {{distinct nontrivial prime factors}} or {{dpf lt n}}
- {{distinct prime factors}} or {{dpf}}
- {{number of distinct prime factors}} or {{little omega}}
- {{sum of distinct prime factors}} or {{sodpf}}
- {{product of distinct prime factors}} or {{squarefree kernel}} or {{radical}} or {{rad}}
- {{multiplicity}}
- {{prime factors (with multiplicity) up to sqrt(n)}} or {{mpf le sqrt(n)}}
- {{nontrivial prime factors (with multiplicity)}} or {{mpf lt n}}
- {{prime factors (with multiplicity)}} or {{mpf}} or {{factorization}}
- {{number of prime factors (with multiplicity)}} or {{big Omega}}
- {{sum of prime factors (with multiplicity)}} or {{sopfr}} or {{integer log}}
- {{product of prime factors (with multiplicity)}} (must give back {{abs|n}}, the absolute value of
)n
- {{quadratfrei}}
- {{Moebius mu}} or {{mu}}
- {{Euler phi}} or {{totient}}
- {{Dedekind psi}}
- {{number of divisors}} or {{sigma 0}} or {{tau}}
- {{sum of divisors}} or {{sigma 1}} or {{sigma}} (Cf. {{divisor function}} or {{sigma k}}, with
(default value))k = 1 - {{divisor function}} or {{sigma k}} (for
)k ≠ 0
External links
- Andrew Hodges, Java Applet for Factorization
- http://factordb.com/
