%N Even numbers such that the number of odd divisors r and the number of even divisors s are both divisors of n.
%C Since s=0 if n is odd, the number n is necessarily even and then s is always a multiple of r. Note that t=r+s may not be a divisor even if both r and s are divisors. For example, if n=144, then r=3, s=12, but t=r+s=15.
%F a(n) = n is even, r = number of odd divisors of n, s = number of even divisors of n, are all divisors of n.
%e a(2)=16 since r=1 and s=4 are both divisors.
%p with(numtheory); A:=: N:=10^4/2: for w to 1 do for k from 2 to N do n:=2*k; S:=divisors(n); r:=nops( select(z->type(z,odd),S) ); s:=nops( select(z->type(z,even),S) ); if andmap(z -> n mod z = 0,[r,s]) then A:=[op(A),n]; print(n,r,s); fi; od od; A;
%Y Cf. A033950, A049439, A057265.
%A _Walter Kehowski_, Jun 24 2006