m = k^2 *j, j<=k, GCD(k,j)=1

[Leroy Quet]

Let a(m) be the number of ways that (ie. the number of (k,j)'s where)

m = k^2 *j,
j <= k,
GCD(k,j)=1,
j and k= positive integers.

So we have the sequence:

{a(m)}: 1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,1,0,0,...

(Not every term is 0 or 1. a(100) = 2.)

And we can also have the sequence, {b(n)}, of m's where a(m) >= 1:

{b(n)}: 1, 4, 9, 16, 18, 25, 36, 48, 49, 50,...

Neither sequence is in the EIS.

I know these sequences might seem a tad arbitrary.
But here is a puzzle (for fun) which might somewhat justify the 
a-sequence:

Evaluate the sum:

sum{m=1 to oo} a(m)/m.


(I'll give the answer in a few days if no one gets it sooner. But someone 
surely will get the {somewhat surprising} answer soon, since this puzzle 
is not extremely difficult.)

thanks,
Leroy Quet