Pairs with common factors
use Prime::Factor;
use Lingua::EN::Numbers;
my \𝜑 = 0, |(1..*).hyper.map: -> \t { t × [×] t.&prime-factors.unique.map: { 1 - 1/$_ } }
sub pair-count (\n) { n × (n - 1) / 2 + 1 - sum 𝜑[1..n] }
say "Number of pairs with common factors - first one hundred terms:\n"
~ (1..100).map(&pair-count).batch(10)».&comma».fmt("%6s").join("\n") ~ "\n";
for ^7 { say (my $i = 10 ** $_).&ordinal.tc.fmt("%22s term: ") ~ $i.&pair-count.&comma }
Output:
Number of pairs with common factors - first one hundred terms:
0 0 0 1 1 4 4 7 9 14
14 21 21 28 34 41 41 52 52 63
71 82 82 97 101 114 122 137 137 158
158 173 185 202 212 235 235 254 268 291
291 320 320 343 363 386 386 417 423 452
470 497 497 532 546 577 597 626 626 669
669 700 726 757 773 818 818 853 877 922
922 969 969 1,006 1,040 1,079 1,095 1,148 1,148 1,195
1,221 1,262 1,262 1,321 1,341 1,384 1,414 1,461 1,461 1,526
1,544 1,591 1,623 1,670 1,692 1,755 1,755 1,810 1,848 1,907
First term: 0
Tenth term: 14
One hundredth term: 1,907
One thousandth term: 195,309
Ten thousandth term: 19,597,515
One hundred thousandth term: 1,960,299,247
One millionth term: 196,035,947,609
Last updated