Duffinian numbers: Difference between revisions
Added Algol 68
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=={{header|ALGOL 68}}==
<lang algol68>BEGIN # find Duffinian numbers: non-primes relatively prime to their divisor count #
INT max number := 500 000; # largest number we will consider #
# iterative Greatest Common Divisor routine, returns the gcd of m and n #
PROC gcd = ( INT m, n )INT:
BEGIN
INT a := ABS m, b := ABS n;
WHILE b /= 0 DO
INT new a = b;
b := a MOD b;
a := new a
OD;
a
END # gcd # ;
# construct a table of the divisor counts #
[ 1 : max number ]INT ds; FOR i TO UPB ds DO ds[ i ] := 1 OD;
FOR i FROM 2 TO UPB ds
DO FOR j FROM i BY i TO UPB ds DO ds[ j ] +:= i OD
OD;
# set the divisor counts of non-Duffinian numbers to 0 #
ds[ 1 ] := 0; # 1 is not Duffinian #
FOR n FROM 2 TO UPB ds DO
IF INT nds = ds[ n ];
nds = n + 1
OR gcd( n, nds ) /= 1
THEN
# n is prime or is n not is relatively prime to its divisor sum #
ds[ n ] := 0
FI
OD;
# show the first 50 Duffinian numbers #
print( ( "The first 50 Duffinian numbers:", newline ) );
INT dcount := 0;
FOR n WHILE dcount < 50 DO
IF ds[ n ] /= 0
THEN # found a Duffinian number #
print( ( " ", whole( n, -3) ) );
IF ( dcount +:= 1 ) MOD 25 = 0 THEN print( ( newline ) ) FI
FI
OD;
print( ( newline ) );
# show the duffinian triplets below UPB ds #
print( ( "The Duffinian triplets up to ", whole( UPB ds, 0 ), ":", newline ) );
dcount := 0;
FOR n FROM 3 TO UPB ds DO
IF ds[ n - 2 ] /= 0 AND ds[ n - 1 ] /= 0 AND ds[ n ] /= 0
THEN # found a Duffinian triplet #
print( ( " (", whole( n - 2, -7 ), " ", whole( n - 1, -7 ), " ", whole( n, -7 ), ")" ) );
IF ( dcount +:= 1 ) MOD 4 = 0 THEN print( ( newline ) ) FI
FI
OD
END</lang>
{{out}}
<pre>
The first 50 Duffinian numbers:
4 8 9 16 21 25 27 32 35 36 39 49 50 55 57 63 64 65 75 77 81 85 93 98 100
111 115 119 121 125 128 129 133 143 144 155 161 169 171 175 183 185 187 189 201 203 205 209 215 217
The Duffinian triplets up to 500000:
( 63 64 65) ( 323 324 325) ( 511 512 513) ( 721 722 723)
( 899 900 901) ( 1443 1444 1445) ( 2303 2304 2305) ( 2449 2450 2451)
( 3599 3600 3601) ( 3871 3872 3873) ( 5183 5184 5185) ( 5617 5618 5619)
( 6049 6050 6051) ( 6399 6400 6401) ( 8449 8450 8451) ( 10081 10082 10083)
( 10403 10404 10405) ( 11663 11664 11665) ( 12481 12482 12483) ( 13447 13448 13449)
( 13777 13778 13779) ( 15841 15842 15843) ( 17423 17424 17425) ( 19043 19044 19045)
( 26911 26912 26913) ( 30275 30276 30277) ( 36863 36864 36865) ( 42631 42632 42633)
( 46655 46656 46657) ( 47523 47524 47525) ( 53137 53138 53139) ( 58563 58564 58565)
( 72961 72962 72963) ( 76175 76176 76177) ( 79523 79524 79525) ( 84099 84100 84101)
( 86527 86528 86529) ( 94177 94178 94179) ( 108899 108900 108901) ( 121103 121104 121105)
( 125315 125316 125317) ( 128017 128018 128019) ( 129599 129600 129601) ( 137287 137288 137289)
( 144399 144400 144401) ( 144721 144722 144723) ( 154567 154568 154569) ( 158403 158404 158405)
( 166463 166464 166465) ( 167041 167042 167043) ( 175231 175232 175233) ( 177607 177608 177609)
( 181475 181476 181477) ( 186623 186624 186625) ( 188497 188498 188499) ( 197191 197192 197193)
( 199711 199712 199713) ( 202499 202500 202501) ( 211249 211250 211251) ( 230399 230400 230401)
( 231199 231200 231201) ( 232561 232562 232563) ( 236195 236196 236197) ( 242063 242064 242065)
( 243601 243602 243603) ( 248003 248004 248005) ( 260099 260100 260101) ( 260641 260642 260643)
( 272483 272484 272485) ( 274575 274576 274577) ( 285155 285156 285157) ( 291599 291600 291601)
( 293763 293764 293765) ( 300303 300304 300305) ( 301087 301088 301089) ( 318095 318096 318097)
( 344449 344450 344451) ( 354481 354482 354483) ( 359551 359552 359553) ( 359999 360000 360001)
( 367235 367236 367237) ( 374543 374544 374545) ( 403201 403202 403203) ( 406801 406802 406803)
( 417697 417698 417699) ( 419903 419904 419905) ( 423199 423200 423201) ( 435599 435600 435601)
( 468511 468512 468513) ( 470449 470450 470451) ( 488071 488072 488073)
</pre>
=={{header|Factor}}==
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