a(n) is the smallest composite k such that Sum_{composites j = 4, ..., k} 1/j exceeds n/2.

Terms

a(0) =8a(1) =16a(2) =33a(3) =63a(4) =118a(5) =216a(6) =395a(7) =715a(8) =1281a(9) =2279a(10) =4036a(11) =7102a(12) =12441a(13) =21722a(14) =37797a(15) =65558a(16) =113422a(17) =195759a(18) =337148a(19) =579465a(20) =994194a(21) =1703072a(22) =2912869a(23) =4975222a(24) =8486672a(25) =14459492a(26) =24608418a(27) =41837580a(28) =71060409a(29) =120585504