Aliquot sequence classifications: Difference between revisions

=={{header|Julia}}==

'''Core Function'''

<lang Julia>

function aliquotclassifier{T<:Integer}(n::T)

a = T[n]

b = divisorsum(a[end])

len = 1

while len < 17 && !(b in a) && 0 < b && b < 2^47+1

push!(a, b)

b = divisorsum(a[end])

len += 1

end

if b in a

1 < len || return ("Perfect", a)

if b == a[1]

2 < len || return ("Amicable", a)

return ("Sociable", a)

elseif b == a[end]

return ("Aspiring", a)

else

return ("Cyclic", push!(a, b))

end

end

push!(a, b)

b != 0 || return ("Terminating", a)

return ("Non-terminating", a)

end

</lang>

'''Supporting Functions'''

<lang Julia>

function pcontrib{T<:Integer}(p::T, a::T)

n = one(T)

pcon = one(T)

for i in 1:a

n *= p

pcon += n

end

return pcon

end

function divisorsum{T<:Integer}(n::T)

dsum = one(T)

for (p, a) in factor(n)

dsum *= pcontrib(p, a)

end

dsum -= n

end

</lang>

'''Main'''

<lang Julia>

println("Classification Tests:")

tests = [1:12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562, 1064, 1488]

for i in tests

(class, a) = aliquotclassifier(i)

println(@sprintf("%8d => ", i), @sprintf("%16s, ", class), a)

end

</lang>

{{out}}

<pre>

Classification Tests:

1 => Terminating, [1,0]

2 => Terminating, [2,1,0]

3 => Terminating, [3,1,0]

4 => Terminating, [4,3,1,0]

5 => Terminating, [5,1,0]

6 => Perfect, [6]

7 => Terminating, [7,1,0]

8 => Terminating, [8,7,1,0]

9 => Terminating, [9,4,3,1,0]

10 => Terminating, [10,8,7,1,0]

11 => Terminating, [11,1,0]

12 => Terminating, [12,16,15,9,4,3,1,0]

28 => Perfect, [28]

496 => Perfect, [496]

220 => Amicable, [220,284]

1184 => Amicable, [1184,1210]

12496 => Sociable, [12496,14288,15472,14536,14264]

1264460 => Sociable, [1264460,1547860,1727636,1305184]

790 => Aspiring, [790,650,652,496]

909 => Aspiring, [909,417,143,25,6]

562 => Cyclic, [562,284,220,284]

1064 => Cyclic, [1064,1336,1184,1210,1184]

1488 => Non-terminating, [1488,2480,3472,4464,8432,9424,10416,21328,22320,55056,95728,96720,236592,459792,881392,882384,1474608,2461648]

</pre>