For n = 10, sigma(n) = 18 and major index (1st definition) of 18 is 5. So, a(10) = 5.

MATHEMATICA

Table[Total@ Flatten@ Position[Partition[IntegerDigits[DivisorSigma[1, n], 2], 2, 1], {1, 0}], {n, 120}] (* Michael De Vlieger, Jan 10 2017, after Harvey P. Dale at A049501 *)