Data update

Task/Mertens-function/COBOL/mertens-function.cob

@@ -0,0 +1,66 @@
+       IDENTIFICATION DIVISION.
+       PROGRAM-ID.  MERTENS.
+
+       DATA DIVISION.
+       WORKING-STORAGE SECTION.
+       01 VARIABLES.
+          03 M             PIC S99 OCCURS 1000 TIMES.
+          03 N             PIC 9(4).
+          03 K             PIC 9(4).
+          03 V             PIC 9(4).
+          03 IS-ZERO       PIC 99 VALUE 0.
+          03 CROSS-ZERO    PIC 99 VALUE 0.
+
+       01 OUTPUT-FORMAT.
+          03 OUT-ITEM.
+             05 OUT-NUM    PIC -9.
+             05 FILLER     PIC X VALUE SPACE.
+          03 OUT-LINE      PIC X(30) VALUE SPACES.
+          03 OUT-PTR       PIC 99 VALUE 4.
+
+       PROCEDURE DIVISION.
+       BEGIN.
+           PERFORM GENERATE-MERTENS.
+           PERFORM WRITE-TABLE.
+           PERFORM COUNT-ZEROES.
+           STOP RUN.
+
+       GENERATE-MERTENS.
+           MOVE 1 TO M(1).
+           PERFORM MERTENS-OUTER-LOOP VARYING N FROM 2 BY 1
+               UNTIL N IS GREATER THAN 1000.
+
+       MERTENS-OUTER-LOOP.
+           MOVE 1 TO M(N).
+           PERFORM MERTENS-INNER-LOOP VARYING K FROM 2 BY 1
+               UNTIL K IS GREATER THAN N.
+
+       MERTENS-INNER-LOOP.
+           DIVIDE N BY K GIVING V.
+           SUBTRACT M(V) FROM M(N).
+
+       WRITE-TABLE.
+           DISPLAY "The first 99 Mertens numbers are: "
+           PERFORM WRITE-ITEM VARYING N FROM 1 BY 1
+               UNTIL N IS GREATER THAN 99.
+
+       WRITE-ITEM.
+           MOVE M(N) TO OUT-NUM.
+           STRING OUT-ITEM DELIMITED BY SIZE INTO OUT-LINE
+               WITH POINTER OUT-PTR.
+           IF OUT-PTR IS EQUAL TO 31,
+               DISPLAY OUT-LINE,
+               MOVE 1 TO OUT-PTR.
+
+       COUNT-ZEROES.
+           PERFORM TEST-N-ZERO VARYING N FROM 2 BY 1
+               UNTIL N IS GREATER THAN 1000.
+           DISPLAY "M(N) is zero " IS-ZERO " times.".
+           DISPLAY "M(N) crosses zero " CROSS-ZERO " times.".
+
+       TEST-N-ZERO.
+           IF M(N) IS EQUAL TO ZERO,
+               ADD 1 TO IS-ZERO,
+               SUBTRACT 1 FROM N GIVING K,
+               IF M(K) IS NOT EQUAL TO ZERO,
+                   ADD 1 TO CROSS-ZERO.

Task/Mertens-function/REXX/mertens-function.rexx

@@ -1,4 +1,4 @@
--- 23 Aug 2025
+-- 3 Mar 2026
 include Setting
 arg xx
 if xx = '' then
@@ -8,14 +8,16 @@ say 'MERTENS FUNCTION'
 say version
 say
 call Tasks1 xx
+call Timer 'R'
 call Tasks2 xx
+call Timer 'R'
 call Tasks3 xx
+call Timer 'R'
 exit
 
 Tasks1:
-procedure expose squa.
+procedure expose squa. memo.
 arg xx
-call Time('r')
 say 'Tasks using Sieve...'
 call Squarefrees 2*xx
 if xx < 100 then
@@ -46,13 +48,11 @@ end
 say
 say 'M1 thru M'xx 'equals zero' a 'times'
 say 'M1 thru M'xx 'crosses zero' b 'times'
-say Format(Time('e'),,3) 'seconds'; say
 return
 
 Tasks2:
-procedure expose squa.
+procedure expose squa. memo.
 arg xx
-call Time('r')
 say 'Tasks using Moebius function...'
 if xx < 100 then
    say 'M1 thru M'xx
@@ -75,13 +75,11 @@ end
 say
 say 'M1 thru M'xx 'equals zero' a 'times'
 say 'M1 thru M'xx 'crosses zero' b 'times'
-say Format(Time('e'),,3) 'seconds'; say
 return
 
 Tasks3:
-procedure expose squa.
+procedure expose squa. memo.
 arg xx
-call Time('r')
 say 'Tasks using Squarefree function...'
 if xx < 100 then
    say 'M1 thru M'xx
@@ -109,7 +107,7 @@ end
 say
 say 'M1 thru M'xx 'equals zero' a 'times'
 say 'M1 thru M'xx 'crosses zero' b 'times'
-say Format(Time('e'),,3) 'seconds'; say
 return
 
+-- Squarefrees; Factors; Even; Odd; Moebius; Timer
 include Math

Task/Mertens-function/Uiua/mertens-function.uiua

@@ -0,0 +1,6 @@
+Moebius ← +0/ׯ≤1⊕⧻⊸⊛°/×
+Mertens ← |1 memo(⨬(+⊃(Mertens-1|Moebius)|1)⊸=1)
+&s↯∞_10≡Mertens↘1⇡101
+⊃(&p$"Crosses zero _ times"/+⌕0_1=0
+| &p$"Equals zero _ times"/+
+)=0≡Mertens↘1⇡1001