Alternating sum of the number of prime factors (counted multiply) of the numbers up to n.

0, 1, 0, 2, 1, 3, 2, 5, 3, 5, 4, 7, 6, 8, 6, 10, 9, 12, 11, 14, 12, 14, 13, 17, 15, 17, 14, 17, 16, 19, 18, 23, 21, 23, 21, 25, 24, 26, 24, 28, 27, 30, 29, 32, 29, 31, 30, 35, 33, 36, 34, 37, 36, 40, 38, 42, 40, 42, 41, 45, 44, 46, 43, 49, 47, 50, 49, 52, 50, 53

1

This sequence appears to be nonnegative. Is there a proof? See S000471 for sums at 2^n.

T. D. Noe, Plot of 1000 terms

T. D. Noe, Table of 1000 terms

Eric W. Weinstein, MathWorld: Distinct Prime Factors

(Mma) Accumulate[Join[{0}, Table[Total[Transpose[FactorInteger[n]][[2]]] (-1)^n, {n, 2, 100}]]]

Cf. A022559, S000468, S000471.

nonn

T. D. Noe, Feb 06 2015