Product of min and max prime factors: Difference between revisions
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;*[[oeis:A066048|OEIS:A066048 - Product of smallest and greatest prime factors of n]] |
;*[[oeis:A066048|OEIS:A066048 - Product of smallest and greatest prime factors of n]] |
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=={{header|ALGOL 68}}== |
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Constructs a tables if min and max prime factors. |
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<syntaxhighlight lang="algol68"> |
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BEGIN # find the product of the min and max prime factors of some numbers # |
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INT max number = 100; # maximum number we will consider # |
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# sieve the primes to max number # |
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[ 0 : max number ]BOOL prime; |
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prime[ 0 ] := prime[ 1 ] := FALSE; |
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prime[ 2 ] := TRUE; |
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FOR i FROM 3 BY 2 TO UPB prime DO prime[ i ] := TRUE OD; |
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FOR i FROM 4 BY 2 TO UPB prime DO prime[ i ] := FALSE OD; |
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FOR i FROM 3 BY 2 TO ENTIER sqrt( UPB prime ) DO |
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IF prime[ i ] THEN |
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FOR s FROM i * i BY i + i TO UPB prime DO prime[ s ] := FALSE OD |
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FI |
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OD; |
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# construct tables of the minimum and maximum prime factors of # |
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# numbers up to max number # |
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[ 1 : max number ]INT min pf; FOR i TO UPB min pf DO min pf[ i ] := 0 OD; |
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[ 1 : max number ]INT max pf; FOR i TO UPB min pf DO max pf[ i ] := 0 OD; |
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min pf[ 1 ] := 1; |
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max pf[ 1 ] := 1; |
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FOR i TO max number DO |
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IF prime[ i ] THEN |
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FOR j FROM i BY i TO UPB min pf DO |
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IF min pf[ j ] = 0 THEN min pf[ j ] := i FI; |
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max pf[ j ] := i |
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OD |
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FI |
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OD; |
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# print the products of the min and max prime factors # |
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FOR i TO max number DO |
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print( ( whole( min pf[ i ] * max pf[ i ], -5 ) ) ); |
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IF i MOD 10 = 0 THEN print( ( newline ) ) FI |
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OD |
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END |
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</syntaxhighlight> |
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{{out}} |
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<pre> |
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1 4 9 4 25 6 49 4 9 10 |
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121 6 169 14 15 4 289 6 361 10 |
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21 22 529 6 25 26 9 14 841 10 |
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961 4 33 34 35 6 1369 38 39 10 |
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1681 14 1849 22 15 46 2209 6 49 10 |
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51 26 2809 6 55 14 57 58 3481 10 |
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3721 62 21 4 65 22 4489 34 69 14 |
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5041 6 5329 74 15 38 77 26 6241 10 |
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9 82 6889 14 85 86 87 22 7921 10 |
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91 46 93 94 95 6 9409 14 33 10 |
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</pre> |
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=={{header|PL/M}}== |
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{{Trans|ALGOL 68}} |
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{{works with|8080 PL/M Compiler}} ... under CP/M (or an emulator) |
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<syntaxhighlight lang="plm"> |
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100H: /* FIND THE PRODUCT OF THE MIN AND MAX PRIME FACTORS OF SOME NUMBERS */ |
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DECLARE FALSE LITERALLY '0', TRUE LITERALLY '0FFH'; |
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/* CP/M SYSTEM CALL AND I/O ROUTINES */ |
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BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END; |
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PR$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END; |
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PR$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END; |
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PR$NL: PROCEDURE; CALL PR$CHAR( 0DH ); CALL PR$CHAR( 0AH ); END; |
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PR$NUMBER: PROCEDURE( N ); /* PRINTS A NUMBER IN THE MINIMUN FIELD WIDTH */ |
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DECLARE N ADDRESS; |
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DECLARE V ADDRESS, N$STR ( 6 )BYTE, W BYTE; |
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V = N; |
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W = LAST( N$STR ); |
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N$STR( W ) = '$'; |
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N$STR( W := W - 1 ) = '0' + ( V MOD 10 ); |
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DO WHILE( ( V := V / 10 ) > 0 ); |
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N$STR( W := W - 1 ) = '0' + ( V MOD 10 ); |
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END; |
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CALL PR$STRING( .N$STR( W ) ); |
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END PR$NUMBER; |
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/* END SYSTEM CALL AND I/O ROUTINES */ |
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DECLARE MAX$N LITERALLY '100', /* MAXIMUM NUMBER TO CONSIDER */ |
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MAX$N$PLUS$1 LITERALLY '101'; /* MAX$N + 1 FOR ARRAY BOUNDS */ |
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/* SIEVE THE PRIMES TO MAX$N */ |
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DECLARE PRIME ( MAX$N$PLUS$1 )BYTE; |
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DO; |
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DECLARE ( I, S ) ADDRESS; |
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PRIME( 0 ), PRIME( 1 ) = FALSE; |
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PRIME( 2 ) = TRUE; |
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DO I = 3 TO LAST( PRIME ) BY 2; PRIME( I ) = TRUE; END; |
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DO I = 4 TO LAST( PRIME ) BY 2; PRIME( I ) = FALSE; END; |
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DO I = 3 TO LAST( PRIME ) / 2 BY 2; |
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IF PRIME( I ) THEN DO; |
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DO S = I + I TO LAST( PRIME ) BY I; PRIME( S ) = FALSE; END; |
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END; |
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END; |
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END; |
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/* CONSTRUCT TABLES OF THE MINIMUM AND MAXIMUM PRIME FACTORS OF NUMBERS */ |
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/* UP TO MAX$N */ |
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DECLARE ( MIN$PF, MAX$PF ) ( MAX$N$PLUS$1 )ADDRESS; |
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DECLARE ( I, J ) BYTE; |
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DECLARE PRODUCT ADDRESS; |
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DO I = 1 TO LAST( MIN$PF ); |
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MIN$PF( I ), MAX$PF( I ) = 0; |
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END; |
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MIN$PF( 1 ) = 1; |
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MAX$PF( 1 ) = 1; |
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DO I = 1 TO MAX$N; |
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IF PRIME( I ) THEN DO; |
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DO J = I TO MAX$N BY I; |
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IF MIN$PF( J ) = 0 THEN MIN$PF( J ) = I; |
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MAX$PF( J ) = I; |
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END; |
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END; |
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END; |
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/* PRINT THE PRODUCTS OF THE MIN AND MAX PRIME FACTORS */ |
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DO I = 1 TO MAX$N; |
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PRODUCT = MIN$PF( I ) * MAX$PF( I ); |
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IF PRODUCT < 10 THEN CALL PR$CHAR( ' ' ); |
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IF PRODUCT < 100 THEN CALL PR$CHAR( ' ' ); |
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IF PRODUCT < 1000 THEN CALL PR$CHAR( ' ' ); |
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CALL PR$CHAR( ' ' ); |
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CALL PR$NUMBER( PRODUCT ); |
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IF I MOD 10 = 0 THEN CALL PR$NL; |
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END; |
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EOF |
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</syntaxhighlight> |
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{{out}} |
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<pre> |
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1 4 9 4 25 6 49 4 9 10 |
|||
121 6 169 14 15 4 289 6 361 10 |
|||
21 22 529 6 25 26 9 14 841 10 |
|||
961 4 33 34 35 6 1369 38 39 10 |
|||
1681 14 1849 22 15 46 2209 6 49 10 |
|||
51 26 2809 6 55 14 57 58 3481 10 |
|||
3721 62 21 4 65 22 4489 34 69 14 |
|||
5041 6 5329 74 15 38 77 26 6241 10 |
|||
9 82 6889 14 85 86 87 22 7921 10 |
|||
91 46 93 94 95 6 9409 14 33 10 |
|||
</pre> |
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=={{header|Raku}}== |
=={{header|Raku}}== |