Alternating sum of the number of prime factors (counted multiply) of the numbers up to 2^n.
0, 1, 2, 5, 10, 23, 49, 103, 213, 444, 900, 1827, 3698, 7477, 15078, 30359, 61052, 122718, 246441, 494733, 992644, 1991022, 3992417, 8003504, 16041096, 32144493, 64403205, 129017037, 258423734, 517570061, 1036483858
0
T. D. Noe, Plot of terms 1..30
(Mma) t = {0}; s = 0; nxt = 2; Do[s = s + Total[Transpose[FactorInteger[n]][[2]]] (-1)^n; If[n == nxt, AppendTo[t, s]; nxt = 2*nxt], {n, 2, 2^16}]; t
Cf. S000469.
nonn
T. D. Noe, Feb 09 2015