%I
%S 2,4,8,16,18,32,36,50,64,72,98,100,128,144,162,196,200,242,256,288,
%T 324,338,392,400,450,484,512,576,578,648,676,722,784,800,882,900,968,
%U 1024,1058,1152,1156,1250,1296,1352,1444,1458,1568,1600,1682,1764,1800,1922
%N Even numbers with odd abundance: even squares or two times squares. Sigma(n)2n=odd means that sigma(n) is also odd.
%C Odd numbers with odd abundance are in A016754. Odd numbers with even abundance are in A088828. Even numbers with even abundance are in A088829.
%H Michael De Vlieger, <a href="/A088827/b088827.txt">Table of n, a(n) for n = 1..10000</a>
%e From _Michael De Vlieger_, May 14 2017: (Start)
%e 4 is a term since it is even and the sum of its divisors {1,2,4} = 7  2(4) = 1 is odd. It is an even square.
%e 18 is a term since it is even and the sum of its divisors {1,2,3,6,9,18} = 39  2(18) = 3 is odd. It is 2 times a square, i.e., 2(9). (End)
%t Do[s=DivisorSigma[1, n]2*n; If[OddQ[s]&&!OddQ[n], Print[{n, s}]], {n, 1, 1000}]
%t (* Second program: *)
%t Select[Range[2, 2000, 2], OddQ[DivisorSigma[1, #]  2 #] &] (* _Michael De Vlieger_, May 14 2017 *)
%Y Cf. A016754, A088828A088829.
%K nonn,easy
%O 1,1
%A _Labos Elemer_, Oct 28 2003
