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.
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