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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. 6
2, 4, 8, 16, 18, 32, 36, 50, 64, 72, 98, 100, 128, 144, 162, 196, 200, 242, 256, 288, 324, 338, 392, 400, 450, 484, 512, 576, 578, 648, 676, 722, 784, 800, 882, 900, 968, 1024, 1058, 1152, 1156, 1250, 1296, 1352, 1444, 1458, 1568, 1600, 1682, 1764, 1800, 1922 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Odd numbers with odd abundance are in A016754. Odd numbers with even abundance are in A088828. Even numbers with even abundance are in A088829.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

EXAMPLE

From Michael De Vlieger, May 14 2017: (Start)

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.

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)

MATHEMATICA

Do[s=DivisorSigma[1, n]-2*n; If[OddQ[s]&&!OddQ[n], Print[{n, s}]], {n, 1, 1000}]

(* Second program: *)

Select[Range[2, 2000, 2], OddQ[DivisorSigma[1, #] - 2 #] &] (* Michael De Vlieger, May 14 2017 *)

CROSSREFS

Cf. A016754, A088828-A088829.

Sequence in context: A154362 A226221 A072462 * A316900 A076057 A133809

Adjacent sequences:  A088824 A088825 A088826 * A088828 A088829 A088830

KEYWORD

nonn,easy

AUTHOR

Labos Elemer, Oct 28 2003

STATUS

approved

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Last modified October 20 02:54 EDT 2019. Contains 328244 sequences. (Running on oeis4.)