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A088827 Even numbers with odd abundance: even squares or two times squares. Sigma(n)-2n=odd means that sigma(n) is also odd. 7

%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, A088828-A088829.

%K nonn,easy

%O 1,1

%A _Labos Elemer_, Oct 28 2003

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Last modified April 15 08:18 EDT 2021. Contains 342977 sequences. (Running on oeis4.)