Product of min and max prime factors: Difference between revisions
Product of min and max prime factors (view source)
Revision as of 22:41, 27 September 2022
, 1 year agoAdded Algol 68 and PL/M
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(Added Algol 68 and PL/M) |
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;*[[oeis:A066048|OEIS:A066048 - Product of smallest and greatest prime factors of n]]
=={{header|ALGOL 68}}==
Constructs a tables if min and max prime factors.
<syntaxhighlight lang="algol68">
BEGIN # find the product of the min and max prime factors of some numbers #
INT max number = 100; # maximum number we will consider #
# sieve the primes to max number #
[ 0 : max number ]BOOL prime;
prime[ 0 ] := prime[ 1 ] := FALSE;
prime[ 2 ] := TRUE;
FOR i FROM 3 BY 2 TO UPB prime DO prime[ i ] := TRUE OD;
FOR i FROM 4 BY 2 TO UPB prime DO prime[ i ] := FALSE OD;
FOR i FROM 3 BY 2 TO ENTIER sqrt( UPB prime ) DO
IF prime[ i ] THEN
FOR s FROM i * i BY i + i TO UPB prime DO prime[ s ] := FALSE OD
FI
OD;
# construct tables of the minimum and maximum prime factors of #
# numbers up to max number #
[ 1 : max number ]INT min pf; FOR i TO UPB min pf DO min pf[ i ] := 0 OD;
[ 1 : max number ]INT max pf; FOR i TO UPB min pf DO max pf[ i ] := 0 OD;
min pf[ 1 ] := 1;
max pf[ 1 ] := 1;
FOR i TO max number DO
IF prime[ i ] THEN
FOR j FROM i BY i TO UPB min pf DO
IF min pf[ j ] = 0 THEN min pf[ j ] := i FI;
max pf[ j ] := i
OD
FI
OD;
# print the products of the min and max prime factors #
FOR i TO max number DO
print( ( whole( min pf[ i ] * max pf[ i ], -5 ) ) );
IF i MOD 10 = 0 THEN print( ( newline ) ) FI
OD
END
</syntaxhighlight>
{{out}}
<pre>
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>
=={{header|PL/M}}==
{{Trans|ALGOL 68}}
{{works with|8080 PL/M Compiler}} ... under CP/M (or an emulator)
<syntaxhighlight lang="plm">
100H: /* FIND THE PRODUCT OF THE MIN AND MAX PRIME FACTORS OF SOME NUMBERS */
DECLARE FALSE LITERALLY '0', TRUE LITERALLY '0FFH';
/* CP/M SYSTEM CALL AND I/O ROUTINES */
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
PR$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END;
PR$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PR$NL: PROCEDURE; CALL PR$CHAR( 0DH ); CALL PR$CHAR( 0AH ); END;
PR$NUMBER: PROCEDURE( N ); /* PRINTS A NUMBER IN THE MINIMUN FIELD WIDTH */
DECLARE N ADDRESS;
DECLARE V ADDRESS, N$STR ( 6 )BYTE, W BYTE;
V = N;
W = LAST( N$STR );
N$STR( W ) = '$';
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL PR$STRING( .N$STR( W ) );
END PR$NUMBER;
/* END SYSTEM CALL AND I/O ROUTINES */
DECLARE MAX$N LITERALLY '100', /* MAXIMUM NUMBER TO CONSIDER */
MAX$N$PLUS$1 LITERALLY '101'; /* MAX$N + 1 FOR ARRAY BOUNDS */
/* SIEVE THE PRIMES TO MAX$N */
DECLARE PRIME ( MAX$N$PLUS$1 )BYTE;
DO;
DECLARE ( I, S ) ADDRESS;
PRIME( 0 ), PRIME( 1 ) = FALSE;
PRIME( 2 ) = TRUE;
DO I = 3 TO LAST( PRIME ) BY 2; PRIME( I ) = TRUE; END;
DO I = 4 TO LAST( PRIME ) BY 2; PRIME( I ) = FALSE; END;
DO I = 3 TO LAST( PRIME ) / 2 BY 2;
IF PRIME( I ) THEN DO;
DO S = I + I TO LAST( PRIME ) BY I; PRIME( S ) = FALSE; END;
END;
END;
END;
/* CONSTRUCT TABLES OF THE MINIMUM AND MAXIMUM PRIME FACTORS OF NUMBERS */
/* UP TO MAX$N */
DECLARE ( MIN$PF, MAX$PF ) ( MAX$N$PLUS$1 )ADDRESS;
DECLARE ( I, J ) BYTE;
DECLARE PRODUCT ADDRESS;
DO I = 1 TO LAST( MIN$PF );
MIN$PF( I ), MAX$PF( I ) = 0;
END;
MIN$PF( 1 ) = 1;
MAX$PF( 1 ) = 1;
DO I = 1 TO MAX$N;
IF PRIME( I ) THEN DO;
DO J = I TO MAX$N BY I;
IF MIN$PF( J ) = 0 THEN MIN$PF( J ) = I;
MAX$PF( J ) = I;
END;
END;
END;
/* PRINT THE PRODUCTS OF THE MIN AND MAX PRIME FACTORS */
DO I = 1 TO MAX$N;
PRODUCT = MIN$PF( I ) * MAX$PF( I );
IF PRODUCT < 10 THEN CALL PR$CHAR( ' ' );
IF PRODUCT < 100 THEN CALL PR$CHAR( ' ' );
IF PRODUCT < 1000 THEN CALL PR$CHAR( ' ' );
CALL PR$CHAR( ' ' );
CALL PR$NUMBER( PRODUCT );
IF I MOD 10 = 0 THEN CALL PR$NL;
END;
EOF
</syntaxhighlight>
{{out}}
<pre>
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>
=={{header|Raku}}==
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