Untouchable numbers: Difference between revisions
Added Perl
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The count of untouchable numbers ≤ 1000000 is: 150232
</pre>
=={{header|Perl}}==
{{libheader|ntheory}}
<lang perl>use strict;
use warnings;
use enum qw(False True);
use ntheory qw/divisor_sum is_prime/;
sub sieve {
my($n) = @_;
my %s;
for my $k (0 .. $n+1) {
my $sum = divisor_sum($k) - $k;
$s{$sum} = True if $sum <= $n+1;
}
%s
}
my(%s,%c);
my($max, $limit, $cnt) = (2000, 1e5, 0);
%s = sieve 14 * $limit;
!is_prime($_) and $c{$_} = True for 1..$limit;
my @untouchable = (2, 5);
for ( my $n = 6; $n <= $limit; $n += 2 ) {
push @untouchable, $n if !$s{$n} and $c{$n-1} and $c{$n-3};
}
map { $cnt++ if $_ <= $max } @untouchable;
print "Number of untouchable numbers ≤ $max : $cnt \n\n" .
(sprintf "@{['%6d' x $cnt]}", @untouchable[0..$cnt-1]) =~ s/(.{84})/$1\n/gr . "\n";
my($p, $count) = (10, 0);
my $fmt = "%6d untouchable numbers were found ≤ %7d\n";
for my $n (@untouchable) {
$count++;
if ($n > $p) {
printf $fmt, $count-1, $p;
printf($fmt, scalar @untouchable, $limit) and last if $limit == ($p *= 10)
}
}</lang>
{{out}}
<pre>Number of untouchable numbers ≤ 2000 : 196
2 5 52 88 96 120 124 146 162 188 206 210 216 238
246 248 262 268 276 288 290 292 304 306 322 324 326 336
342 372 406 408 426 430 448 472 474 498 516 518 520 530
540 552 556 562 576 584 612 624 626 628 658 668 670 708
714 718 726 732 738 748 750 756 766 768 782 784 792 802
804 818 836 848 852 872 892 894 896 898 902 926 934 936
964 966 976 982 996 1002 1028 1044 1046 1060 1068 1074 1078 1080
1102 1116 1128 1134 1146 1148 1150 1160 1162 1168 1180 1186 1192 1200
1212 1222 1236 1246 1248 1254 1256 1258 1266 1272 1288 1296 1312 1314
1316 1318 1326 1332 1342 1346 1348 1360 1380 1388 1398 1404 1406 1418
1420 1422 1438 1476 1506 1508 1510 1522 1528 1538 1542 1566 1578 1588
1596 1632 1642 1650 1680 1682 1692 1716 1718 1728 1732 1746 1758 1766
1774 1776 1806 1816 1820 1822 1830 1838 1840 1842 1844 1852 1860 1866
1884 1888 1894 1896 1920 1922 1944 1956 1958 1960 1962 1972 1986 1992
2 untouchable numbers were found ≤ 10
5 untouchable numbers were found ≤ 100
89 untouchable numbers were found ≤ 1000
1212 untouchable numbers were found ≤ 10000
13863 untouchable numbers were found ≤ 100000</pre>
=={{header|Phix}}==
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