[seqfan] d(a(n)) = d(a(n)-a(n-1))

[Leroy Quet]

Consider these three sequences I just submitted:

%I A160689
%S A160689 1,2,2,2,8,2,2,8,2,2,8,2,2,8,2,21,5
%N A160689 a(1)=1. a(n) = the smallest positive integer such that d(a(n)) = d(sum{k=1 to n} a(k)), where d(m) = the number of divisors of m. 
%C A160689 sum{k=1 to n} a(k) = A160690(n). d(A160689(n)) = d(A160690(n)) = A160691(n). 
%Y A160689 A160690,A160691 
%K A160689 more,nonn
%O A160689 1,2

%I A160690
%S A160690 1,3,5,7,15,17,19,27,29,31,39,41,43,51,53,74,79
%N A160690 a(1)=1. a(n) = the smallest integer > a(n-1) such that d(a(n)) = d(a(n)-a(n-1)), where d(m) = the number of divisors of m. 
%C A160690 A160690(n)-A160690(n-1) = A160689(n), for n >= 2. d(A160689(n)) = d(A160690(n)) = A160691(n). 
%Y A160690 A160689,A160691 
%K A160690 more,nonn
%O A160690 1,2

%I A160691
%S A160691 1,2,2,2,4,2,2,4,2,2,4,2,2,4,2,4,2
%N A160691 a(n) = the number of divisors of A160689(n) = the number of divisors of A160690(n). 
%Y A160691 A160689,A160690 
%K A160691 more,nonn
%O A160691 1,2

Does every positive integer occur in A160691?

If so, could someone calculate a few of the terms of the sequence {b(k)},T where b(n) = the smallest positive integer such that A160691(b(n)) = n?

Thanks,
Leroy Quet