Generally speaking, how many days after sex can a blood pregnancy test pick up pregnancy? (my cycle is about 40 days long?

Probably 2 weeks from the time of sexual encounter. If it still is negative after 3 weeks of sexual encounter, pregnancy is almost ruled out.

Conception occurs within day or so of the sex. It takes about 3 weeks for the embryo to make enough HCG for a positive pregnancy test. Blood test may be done a day after a missed period. Home pregnancy tests should be done 4-5 days after the missed period. If the result is negative repeat the test in 4-5 days. Use first morning urine and follow instructions for the test carefully.