sdiv =: */ @: (((^>:) %&<: [)/) @: (__&q:) sdiv1 =: */ @ (%~/) @: <: @ ((^>:)/\) @ (__&q:) sdiv2 =: (((^>:) */@:%&:<: [)/) @: (__&q:) sdiv3 =: __ ((^>:) */@:%&:<: [)/@q: ] sdiv4 =: (*//.~ (* */@:%&:<: ]) ~.)@q:
(sdiv -: sdiv1) !20x 1 (sdiv -: sdiv2) !20x 1 (sdiv -: sdiv3) !20x 1 (sdiv -: sdiv4) !20x 1 On Tue, Jun 10, 2014 at 1:54 PM, Henry Rich <[email protected]> wrote: > Shorter version: > > sdiv =. */@(%~/)@:<:@((^ >:)/\)@(__&q:) > > spdiv =. (-~ sdiv) > spdiv 12 > 16 > > Henry Rich > On 6/10/2014 3:09 PM, Henry Rich wrote: > >> NB. sum of divisors >> sdiv =. (*/) @: (((^ >:) %&<: [)/) @: (__&q:) >> NB. sum of proper divisors >> spdiv =. (-~ sdiv) >> spdiv 12 >> 16 >> >> Henry Rich >> >> On 6/10/2014 1:18 PM, Roger Hui wrote: >> >>> From http://www.jsoftware.com/jwiki/Essays/Divisors >>>> >>> >>> div=: /:~ @: , @: > @: (*/&.>/) @: ((^ i.@>:)&.>/) @: (__&q:) >>> div 360 >>> 1 2 3 4 5 6 8 9 10 12 15 18 20 24 30 36 40 45 60 72 90 120 180 360 >>> >>> >>> >>> >>> >>> On Tue, Jun 10, 2014 at 10:10 AM, Jon Hough <[email protected]> wrote: >>> >>> My attempt at making a verb that finds the total of all proper >>>> divisors of >>>> an integer seems to work. >>>> e.g. if n = 12, the sum of proper divisors is 1 +2 +3+4+6 = 16 (note >>>> 12 is >>>> not included) >>>> This verb is actually equal to the "sigma function" minus n.Wikipedia >>>> explanation: http://en.wikipedia.org/wiki/Divisor_function >>>> (I essentially used the equation for sigma_x(n) where x = 1) >>>> my verb: >>>> >>>> sum =.(((*/@:-&1@:{.)%~(*/@:-&1@:({.^(1&+@:,@:}.))))@:(2&p:))-] >>>> This seems ok, but is not aesthetically pleasing, and seems to be very >>>> bracketty, and given that the mathematical equation is pretty concise >>>> I am >>>> surprised the J verb is so long. If anyone knows a nicer way of doing >>>> this >>>> I would be grateful to see it. >>>> Regards. >>>> ---------------------------------------------------------------------- >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>> >>>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >>> >>> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> >> ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
