Composites Of This Sequence

[Leroy Quet]

I just submitted the following (which has yet to appear):

%I A143578
%S A143578 1,2,3,5,7,11,13,15,17,19,23,29,31,35,37,41,43,47
%N A143578 A positive integer n is included if (j+n/j) divides (k+n/k) for every divisor k of n, where j is the largest divisor of n that is <= sqrt(n).
%C A143578 This sequence trivially contains all the primes.
%e A143578 The divisors of 35 are 1,5,7,35. The sum of the two middle divisors is 5+7 = 12. 12 divides 7 + 35/7 = 5+35/5 = 12, of course. And 12 divides 1 + 35/1 = 35 +35/35 = 36. So 35 is in the sequence.
%Y A143578 A063655
%O A143578 1
%K A143578 ,more,nonn,

What is the sequence of composites of A143578?

It begins: 15, 35,...


And, another possible sequence: a(n) = the first term of A143578 with 2n divisors.

2, 15,...
(1 is the only square in the sequence, since m is coprime to m^2 +1.)

Thanks,
Leroy Quet