Initial data commit

Task/Mertens-function/Zkl/mertens-function-1.zkl

@@ -0,0 +1,25 @@
+fcn mertensW(n){
+   [1..].tweak(fcn(n,pm){
+      pm.incN(mobius(n));
+      pm.value
+   }.fp1(Ref(0)))
+}
+fcn mobius(n){
+   pf:=primeFactors(n);
+   sq:=pf.filter1('wrap(f){ (n % (f*f))==0 });  // False if square free
+   if(sq==False){ if(pf.len().isEven) 1 else -1 }
+   else 0
+}
+fcn primeFactors(n){  // Return a list of prime factors of n
+   acc:=fcn(n,k,acc,maxD){  // k is 2,3,5,7,9,... not optimum
+      if(n==1 or k>maxD) acc.close();
+      else{
+	 q,r:=n.divr(k);   // divr-->(quotient,remainder)
+	 if(r==0) return(self.fcn(q,k,acc.write(k),q.toFloat().sqrt()));
+	 return(self.fcn(n,k+1+k.isOdd,acc,maxD))  # both are tail recursion
+      }
+   }(n,2,Sink(List),n.toFloat().sqrt());
+   m:=acc.reduce('*,1);      // mulitply factors
+   if(n!=m) acc.append(n/m); // opps, missed last factor
+   else acc;
+}

Task/Mertens-function/Zkl/mertens-function-2.zkl

@@ -0,0 +1,9 @@
+mertensW().walk(199)
+.pump(Console.println, T(Void.Read,19,False),
+	fcn{ vm.arglist.pump(String,"%3d".fmt) });
+
+println("\nIn the first 1,000 terms of the Mertens sequence there are:");
+otm:=mertensW().pump(1_000,List);
+otm.reduce(fcn(s,m){ s + (m==0) },0) : println(_," zeros");
+otm.reduce(fcn(p,m,rs){ rs.incN(m==0 and p!=0); m }.fp2( s:=Ref(0) ));
+println(s.value," zero crossings");