Number of distinct exponentials

[Nick Hobson]

Hi Seqfans,

What do you think of this sequence: 1, 3, 7, 11, 19, 28, 40, 50, 60, 76,  
96, 115, 139, 163, 189, 207, 239, 270, 306, 340, 378, 417, 461, 503, 539,  
585, 621, 670, 726, 779, 839, 881, 941, ... ?

It is the number of distinct terms i^j for 1 <= i,j <= n.  (Cf. A027424).   
I don't have a formula for the sequence, or any nice bounds, such as those  
for A027424.

Similarly, the corresponding sequence for 2 <= i,j <= n may be of  
interest?  (1, 4, 8, 15, 23, 34, 44, 54, 69, 88, 106, 129, 152, 177, 195,  
226, 256, 291, 324, 361, 399, 442, 483, 519, 564, 600, 648, 703, 755, 814,  
856, 915, 976, ... .)  A complementary sequence is n^2 - a(n): the number  
of duplicates (0, 0, 1, 1, 2, 2, 5, 10, 12, 12, ...), but is it worth  
adding both?

PARI script for 1 <= i,j <= n:
g(lim)={local(z,x,c,f); z=listcreate(lim^2); vector(lim, m, for(i=1, m,  
for(j=1, m, x=factor(i); x[,2]*=j; c=Str(x); f=setsearch(z, c, 1); if(f,  
listinsert(z, c, f)))); #z)};
g(100)

Nick