Data commit

Task/Perfect-numbers/M2000-Interpreter/perfect-numbers.m2000

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+Module PerfectNumbers {
+      Function Is_Perfect(n as decimal) {
+            s=1 : sN=Sqrt(n)
+            last= n=sN*sN
+            t=n
+            If n mod 2=0 then s+=2+n div 2
+            i=3 : sN--
+            While i<sN {
+            if  n mod i=0 then t=n div i :i=max.data(n div t, i): s+=t+ i
+            i++
+            }
+            =n=s
+      }
+      Inventory Known1=2@, 3@
+      IsPrime=lambda  Known1 (x as decimal) -> {
+                  =0=1
+                  if exist(Known1, x) then =1=1 : exit
+                  if x<=5 OR frac(x) then {if x == 2 OR x == 3 OR x == 5 then Append Known1, x  : =1=1
+                  Break}
+                  if frac(x/2) else exit
+                  if frac(x/3) else exit
+                  x1=sqrt(x):d = 5@
+                  {if frac(x/d ) else exit
+                        d += 2: if d>x1 then Append Known1, x : =1=1 : exit
+                        if frac(x/d) else exit
+                        d += 4: if d<= x1 else Append Known1, x :  =1=1: exit
+                   loop}
+            }
+      \\ Check a perfect and a non perfect number
+      p=2 : n=3 : n1=2
+      Document Doc$
+      IsPerfect( 0, 28)
+      IsPerfect( 0, 1544)
+      While p<32  { ' max 32
+            if isprime(2^p-1@) then {
+                   perf=(2^p-1@)*2@^(p-1@)
+                   Rem  Print perf
+                   \\ decompose pretty fast the Perferct Numbers
+                   \\ all have a series of 2 and last a prime equal to perf/2^(p-1)
+                   inventory queue factors
+                   For i=1 to p-1 {
+                         Append factors, 2@
+                  }
+                  Append factors, perf/2^(p-1)
+                  \\ end decompose
+                  Rem Print factors
+                  IsPerfect(factors, Perf)
+            }
+            p++
+      }
+
+      Clipboard Doc$
+      \\ exit here. No need for Exit statement
+      Sub IsPerfect(factors, n)
+            s=false
+            if n<10000 or type$(factors)<>"Inventory" then {
+                  s=Is_Perfect(n)
+            } else {
+                  local mm=each(factors, 1, -2), f =true
+                  while mm {if eval(mm)<>2 then f=false
+                  }
+                  if f then if n/2@**(len(mm)-1)= factors(len(factors)-1!) then s=true
+            }
+            Local a$=format$("{0} is {1}perfect number", n, If$(s->"", "not "))
+            Doc$=a$+{
+            }
+            Print a$
+      End Sub
+}
+
+PerfectNumbers