open in, "rep_set_ass_tax.fna"; 
 
 while ($line=<in>) { 
   if($line=~/>/) {
 
    @vettore=split(/\s+/, $line); 
    open my $fh, ">>seq_id.txt" or die "Cannot open output.txt: $!"; # There is no need to open a file each time you need to print something into it if it is the same file. just open it once before the loop and print to it 
    foreach (@vettore); # What is a loop and what is a proper way to write one. So you started a loop and what are you going to do with it(I mean variables in the loop)
      print $_ . "\n"; # OK, so you want to print something, but where to STDOUT or into a file that you have opened
    close my $fh; # again my doesn't have any effect if use strict is not called.
    } 
 }


##</code><code>##

use strict;
use warnings;

open(IN, "<", "rep_set_ass_tax.fna") or die "Died!!"; 
open (OUT , ">","seq_id.txt") or die "Cannot open output.txt: $!";
 while (my $line=<IN>) { 
   if($line=~/>/) {
 
      my @vettore=split(" ", $line); 
    
      foreach (@vettore){ 
       print OUT $_ . "\n"; 
      }
   } 
 }
 
 close IN;
 close OUT;

##</code><code>##

use strict;
use warnings;

open(IN, "<", "rep_set_ass_tax.fna") or die "Died!!"; 

 while (my $line=<IN>) { 
   if($line=~/>(\d+)/) {
     print $1 . "\n";
   } 
 }
 
 close IN;


##</code><code>##

>1
ATGT...
>2
ATGGTGC..

##</code><code>##

use strict; 
use warnings; 
my $infile = "rep_set_ass_tax.fna";
my $outfile = "seq_id.txt";  # you need to open this only if writing to a file 

open(IN, "<", $infile) or die "Died!!"; 


while (my $line=<IN>) { 
  if($line=~/>\s*(\d+)/) {
     print $1 . "\n"; 
  } 
} 
close IN;