Powerful numbers: Difference between revisions
→{{header|Perl 6}}: Add a Perl 6 example
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Number of 10-powerful <= 10^j for 0 <= j < 20: {1, 1, 1, 1, 5, 9, 14, 21, 28, 43, 68, 104, 155, 227, 322, 447, 621, 858, 1192, 1651}
</pre>
=={{header|Perl 6}}==
{{works with|Rakudo|2020.01}}
{{trans|Perl}}
Perl 6 has no handy pre-made nth integer root routine so has the same problem as Go with needing a slight "fudge factor" in the nth root calculation.
<lang perl6>sub super ($e) { $e.trans([<0123456789>.comb] => [<⁰¹²³⁴⁵⁶⁷⁸⁹>.comb]) }
sub is-square-free (Int $n) {
constant @p = ^100 .map: { next unless .is-prime; .² };
return False if $n %% $_ for @p;
True
}
my $fudge-factor = .0001;
sub powerfuls ($n, $k) {
my @powerful;
p(1, 2*$k - 1);
sub p ($m, $r) {
@powerful.push($m), return if $r < $k;
for 1 .. (($n / $m) ** (1/$r) + $fudge-factor).floor -> $v {
if $r > $k {
next unless is-square-free($v);
next unless $m gcd $v == 1;
}
p($m * $v ** $r, $r - 1)
}
}
@powerful;
}
put "First and last five enumerated n-powerful numbers in 10ⁿ:";
for 2..10 -> \k {
my @powerful = sort powerfuls(10**k, k);
printf "%2d %2s-powerful numbers <= 10%-2s: %s ... %s\n", +@powerful, k, super(k),
@powerful.head(5).join(", "), @powerful.tail(5).join(", ");
}
put "\nCounts in each order of magnitude:";
my $top = 10;
for 2..10 -> \k {
my @powerfuls = powerfuls(10**($top+k), k);
printf "%2s-powerful numbers <= 10ⁿ (where n == 0 through %d): ", k, $top+k;
say join ", ", (0 ..^ ($top+k)).hyper(:2batch).map: -> \j { +@powerfuls.race.grep: * <= 10**j }
}</lang>
{{out}}
<pre>First and last five enumerated n-powerful numbers in 10ⁿ:
14 2-powerful numbers <= 10² : 1, 4, 8, 9, 16 ... 49, 64, 72, 81, 100
20 3-powerful numbers <= 10³ : 1, 8, 16, 27, 32 ... 625, 648, 729, 864, 1000
25 4-powerful numbers <= 10⁴ : 1, 16, 32, 64, 81 ... 5184, 6561, 7776, 8192, 10000
32 5-powerful numbers <= 10⁵ : 1, 32, 64, 128, 243 ... 65536, 69984, 78125, 93312, 100000
38 6-powerful numbers <= 10⁶ : 1, 64, 128, 256, 512 ... 559872, 746496, 823543, 839808, 1000000
46 7-powerful numbers <= 10⁷ : 1, 128, 256, 512, 1024 ... 7558272, 8388608, 8957952, 9765625, 10000000
52 8-powerful numbers <= 10⁸ : 1, 256, 512, 1024, 2048 ... 60466176, 67108864, 80621568, 90699264, 100000000
59 9-powerful numbers <= 10⁹ : 1, 512, 1024, 2048, 4096 ... 644972544, 725594112, 816293376, 967458816, 1000000000
68 10-powerful numbers <= 10¹⁰: 1, 1024, 2048, 4096, 8192 ... 7739670528, 8589934592, 8707129344, 9795520512, 10000000000
Counts in each order of magnitude:
2-powerful numbers <= 10ⁿ (where n == 0 through 12): 1, 4, 14, 54, 185, 619, 2027, 6553, 21044, 67231, 214122, 680330
3-powerful numbers <= 10ⁿ (where n == 0 through 13): 1, 2, 7, 20, 51, 129, 307, 713, 1645, 3721, 8348, 18589, 41136
4-powerful numbers <= 10ⁿ (where n == 0 through 14): 1, 1, 5, 11, 25, 57, 117, 235, 464, 906, 1741, 3312, 6236, 11654
5-powerful numbers <= 10ⁿ (where n == 0 through 15): 1, 1, 3, 8, 16, 32, 63, 117, 211, 375, 659, 1153, 2000, 3402, 5770
6-powerful numbers <= 10ⁿ (where n == 0 through 16): 1, 1, 2, 6, 12, 21, 38, 70, 121, 206, 335, 551, 900, 1451, 2326, 3706
7-powerful numbers <= 10ⁿ (where n == 0 through 17): 1, 1, 1, 4, 10, 16, 26, 46, 77, 129, 204, 318, 495, 761, 1172, 1799, 2740
8-powerful numbers <= 10ⁿ (where n == 0 through 18): 1, 1, 1, 3, 8, 13, 19, 32, 52, 85, 135, 211, 315, 467, 689, 1016, 1496, 2191
9-powerful numbers <= 10ⁿ (where n == 0 through 19): 1, 1, 1, 2, 6, 11, 16, 24, 38, 59, 94, 145, 217, 317, 453, 644, 919, 1308, 1868
10-powerful numbers <= 10ⁿ (where n == 0 through 20): 1, 1, 1, 1, 5, 9, 14, 21, 28, 43, 68, 104, 155, 227, 322, 447, 621, 858, 1192, 1651</pre>
=={{header|Sidef}}==
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