A024455 [ (3rd elementary symmetric function of P(n))/(2nd elementary symmetric function of P(n)) ], where P(n) = {first n+2 primes}.

0, 2, 4, 7, 11, 17, 23, 30, 39, 50, 61, 74, 88, 104, 121, 140, 160, 182, 204, 228, 254, 282, 312, 343, 376, 409, 444, 480, 519, 561, 604, 648, 695, 743, 793, 845, 898, 954, 1011, 1069, 1130, 1192, 1256