There is some speed to gain at the cost of space by making the sigma
test tacit.
ts '(#~zumkeller) 6+i.4995'
4.648012 143936
ts '(#~zumkeller2) 6+i.4995'
1.412875 441408
((#~zumkeller)-:(#~zumkeller2)) 6+i.4995
1
=========== Code ================
sigmaTest=: 4 : 0
if. 0=x do.1 return.end.
if. 0=#y do.0 return.end.
f=.{.y
fs=.}.y
if. x<f do. x sigmaTest fs return.end.
if. (x-f) sigmaTest fs do.1 return.end.
x sigmaTest fs
)
zumkeller =: 3 : 0 " 0
s=. +/ fs=. divs y
if. (2|s) +. s < +: y do. 0
else. fs sigmaTest~ s&-&.+:y end.
)
sigmat =: [(($:}.)`1:@.((-{.)$:}...@]))`0:@.(0...@])`1:@.(0=[)>:#]
zumkeller2 =: 3 : 0 " 0
s=. +/ fs=. divs y
if. (2|s) +. s < +: y do. 0
else. fs sigmat~ s&-&.+:y end.
)
--
Met vriendelijke groet,
=@@i
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