Of Different Prime-Factorization Exponents

[Leroy Quet]

A couple of days ago I sent to the EIS this sequence:

>%S A000001 0,1,2,3,4,3,6,7,8,6,10,8,12,9
>%N A000001 If n = product{p=primes,p|n} p^b(n,p), where each b(n,p) is a 
>positive integer, then a(n) is number of positive integers m, m < n, 
>such that each b(m,p) does not equal b(n,p).
>%e A000001 12 = 2^2 * 3^1. Of the positive integers < 12, there are 8 
>integers where no prime divides these integers the same number of times 
>the prime divides 12: 1, 2 = 2^1, 5 = 5^1, 7 = 7^1, 8 = 2^3, 9 = 3^2, 10 = 
>2^1 *5^1, and 11 = 11^1.
>So a(12) = 8.
>The other positive integers < 12 (3 = 3^1, 4 = 2^2, and 6 = 2^1 
>* 3^1) each are divisible by at least one prime the same number of times 
>this prime divides 12.
>%O A000001 1
>%K A000001 ,more,nonn,

(Unfortunately, this sequence has not yet appeared, given that Neil is 
currently on vacation.)

Is there a direct way (say, a sum involving the Moebius function, 
perhaps) to calculate this sequence's terms?

If someone finds a formula, please post it as a comment to this sequence 
when the sequence finally appears (as well as posting it to seq.fan).
I myself am not as good at math as I used to be, and cannot find a 
formula for a(n).

thanks,
Leroy Quet