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Numbers n such that the number of odd divisors of (2n)^2 is an odd divisor of (2n)^2, and the number of even divisors of (2n)^2 is an even divisor of (2n)^2.
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%I #6 Mar 31 2012 13:22:29

%S 1,2,3,6,8,12,15,21,24,25,30,33,39,42,45,50,51,57,66,69,75,78,81,87,

%T 90,93,96,102,111,114,120,123,128,129,138,141,150,159,162,168,174,177,

%U 180,183,186,189,200,201,213,219,222,225,237,240,246,249,258,264,267,282,291,300

%N Numbers n such that the number of odd divisors of (2n)^2 is an odd divisor of (2n)^2, and the number of even divisors of (2n)^2 is an even divisor of (2n)^2.

%C A016742(a(n)) = A181795(n)

%p for j from 1 to 300 do

%p y:=(2*j)^2:evdiv:=0:oddiv:=0:

%p for k in divisors(y) do

%p if(k mod 2=0)then evdiv:=evdiv+1:else oddiv:=oddiv+1:fi:

%p od:

%p if(type(y/evdiv,integer) and type(y/oddiv,integer))then

%p print(j);

%p fi;

%p od:

%K easy,nonn

%O 1,2

%A _Nathaniel Johnston_, Nov 17 2010