to generalize the problem by passing the moduli along as arguments.
If I've understood the task correctly, I think you're working the math too hard:
sub x{ my $v=shift; my $t=0; $t += !!($v%$_) for @_; return $t!=@_ };;
sub fn{ my$n; x($_, @_) and $n+=$_ for 1 .. shift; $n };;
print fn( 10, 3, 5 );;
33
print fn( 10, 3, 5, 7 );;
40
print fn( 100000, 3, 5, 7, 74017, 74027, 74047, 74077 );;
2714660445
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