# Favour shortest sequence.
my $thresh = 1; # Match *more than* $thresh times.
while (<DATA>) {
  chomp;
  while (/((.{1,6}?)\2{$thresh,})/g) {
    printf( "Found %d %-6s (length=%d, total=%2d) at pos %2d in %s\n",
      length($1) / length($2), # Number of matches.
      $2,                      # Sequence.
      length($2),              # Length of sequence.
      length($1),              # Length of match.
      $-[0],                   # Start position.
      $_                       # String we're searching.
    );
  }
}

__DATA__
CATCATCATCATCAT
AAAGTCAAAGTCAAAGTC

gives:
Found 5 CAT    (length=3, total=15) at pos  0 in CATCATCATCATCAT
Found 3 A      (length=1, total= 3) at pos  0 in AAAGTCAAAGTCAAAGTC
Found 2 GTCAAA (length=6, total=12) at pos  3 in AAAGTCAAAGTCAAAGTC