Does this do what you want?

my $thresh = 3; # as per Ikegami's note, pattern must repeat MORE THAN
+ this many times
while (<DATA>) {
  while (/((.{1,6})\2{$thresh,})/g) {
    printf "$2 (length=%d) repeats in $1\n", length $2;
    printf "Found at $-[0] to %d in $_", pos()-1;
  }
}

__DATA__
GATTATTATTATTATTATTGCATATATATAGCAAAAAATTTTTTGC
ATATTATATTATATTATATTGC
ATAGACATAGACATAGAC
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