Bash + GNU utilities, 86(削除) 86 (削除ここまで) 85 bytes
for((k=4;k<1ドル;k++,j=k-2)){ [ $(factor`factor $k $j|wc -w)w` = 4 ]&&x=$x+1/$k+1/$j;};bc -l<<<0$x
Constructs a large arithmetic expression and then feeds it to bc -l to evaluate it.
Edit: Mistakenly left in a $(...) pair from an old version with nested command substitution; changed to backticks to save a byte.
Bash + GNU utilities, 86 bytes
for((k=4;k<1ドル;k++,j=k-2)){ [ $(factor $k $j|wc -w) = 4 ]&&x=$x+1/$k+1/$j;};bc -l<<<0$x
Constructs a large arithmetic expression and then feeds it to bc -l to evaluate it.
Bash + GNU utilities, (削除) 86 (削除ここまで) 85 bytes
for((k=4;k<1ドル;k++,j=k-2)){ [ `factor $k $j|wc -w` = 4 ]&&x=$x+1/$k+1/$j;};bc -l<<<0$x
Constructs a large arithmetic expression and then feeds it to bc -l to evaluate it.
Edit: Mistakenly left in a $(...) pair from an old version with nested command substitution; changed to backticks to save a byte.
Bash + GNU utilities, 86 bytes
for((k=4;k<1ドル;k++,j=k-2)){ [ $(factor $k $j|wc -w) = 4 ]&&x=$x+1/$k+1/$j;};bc -l<<<0$x
Constructs a large arithmetic expression and then feeds it to bc -l to evaluate it.