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Count how many numbers are divisible by perfect numbers in a given range

Given two arbitrary integers \$a\$ and \$b\$, count how many numbers are divisible by perfect numbers in that given range (\$a\$ and \$b\$ both are inclusive).

In mathematics, a perfect number is a positive integer that is the sum of its proper positive divisors, that is, the sum of the positive divisors excluding the number itself.Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself), or \$σ(n) = 2n\$.

Input:

1 100

Output:

Use stdin and stdout for Input/Output
Your code must handle big integers, so it is not good enough to hard-code a list of perfect numbers.
Shortest code wins

Answer*

# [Perl 5] `-MList::Util=sum,any -pl`, 77 bytes



 $"=$_,$\+=any{$"%$_==0}grep{//;2*$_==sum grep{$'%$_==0}1..$_}2..$"for$_..<>}{

[Try it online!][TIO-kj0vdmgx]

[Perl 5]: https://www.perl.org/
[TIO-kj0vdmgx]: https://tio.run/##K0gtyjH9/19FyVYlXkclRts2Ma@yWkVJVSXe1tagNr0otaBaX9/aSAvELy7NVQCLqKhD5Q319FTia42ApFJafpFKvJ6ejV1t9f//hlyGBgb/8gtKMvPziv/r@vpkFpdYWYWWZOaADNEB2vFftyAHAA "Perl 5 – Try It Online"


Ungolfed:
<pre>$_ = <>; # implicit by -p command line switch
for$_($_..<>){ # loop over the range from $_ to the next input
 $"=$_; # store a copy of the current number ($_) so it can be used in sub-loops
 $\+= # counter for number of perfectly divisible numbers found
 any{$"%$_==0} # check if the current number ($") is evenly divisible by a:
 grep{//;2*$_== # PERFECT NUMBER: a number where twice the number equals
 sum grep{$'%$_==0}1..$_ # the sum of the numbers which divide it evenly
 }2..$" # that exists in range of 2 to the current number
}
print$\; # implicit by -p command line switch</pre>

If this is an answer to a challenge…

…Be sure to follow the challenge specification. However, please refrain from exploiting obvious loopholes. Answers abusing any of the standard loopholes are considered invalid. If you think a specification is unclear or underspecified, comment on the question instead.
…Try to optimize your score. For instance, answers to code-golf challenges should attempt to be as short as possible. You can always include a readable version of the code in addition to the competitive one. Explanations of your answer make it more interesting to read and are very much encouraged.
…Include a short header which indicates the language(s) of your code and its score, as defined by the challenge.

More generally…

…Please make sure to answer the question and provide sufficient detail.
…Avoid asking for help, clarification or responding to other answers (use comments instead).

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