2 number-theoretical sequences

[Leroy Quet]

I just submitted the 2 following sequences to the OEIS:


>%S A000001 12,24,40,45,48,56,63,80,90,96,112
>%N A000001 Largest prime-power dividing n is not a power of the largest 
>prime dividing n.
>%e A000001 45 is included because 45 = 3^2 *5, and 5 (the largest prime 
>dividing 45) is less than 9 (the largest prime-power dividing 45).
>%O A000001 0
>%K A000001 ,more,nonn,


>%S A000001 2,3,5,6,7,10,11,12,13,14,15,17,19,20,21,22,23,24,26,28,29,30
>%N A000001 Square of largest prime dividing n does not divide n.
>%e A000001 63 is included because 63 = 3^2 *7, and 7 (the largest prime 
>dividing 63) only divides 63 once.
>%O A000001 0
>%K A000001 ,more,nonn,

Now, the latter sequence is simply every integer >= 2 not in sequence 
A070003.

I wonder about such things as
what are the asymptotics for these sequences.

I know there must be some interesting questions that can be asked and 
answered about these sequences, but I am not currently aware of any.

If {a(k)} is the latter sequence, then

sum 1/a(k)^r =

sum{p=primes} (1/p^r) /product{q=primes<p} (1 -1/q^r).

(right? Simple, but I may have made a stupid mistake.)

thanks,
Leroy Quet