# Input: $max >= 1
# Output: an array of size $max with $max mertenNumbers beginning with 1
def mertensNumbers:
. as $max
| reduce range(2; $max + 1) as $n ( [1];
.[$n-1]=1
| reduce range(2; $n+1) as $k (.;
.[$n-1] -= .[($n / $k) | floor - 1] ));