The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A088829

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A088829

Even numbers with even abundance.
(history; published version)

#8 by Giovanni Resta at Sat Sep 21 06:55:18 EDT 2019

STATUS

proposed

approved

#7 by Amiram Eldar at Sat Sep 21 06:28:42 EDT 2019

STATUS

editing

proposed

#6 by Amiram Eldar at Sat Sep 21 06:10:32 EDT 2019

LINKS

Amiram Eldar, <a href="/A088829/b088829.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

#5 by N. J. A. Sloane at Tue Oct 15 22:32:19 EDT 2013

AUTHOR

_Labos E. (labos(AT)ana.sote.hu), Elemer_, Oct 28 2003

Discussion

Tue Oct 15

22:32

OEIS Server: https://oeis.org/edit/global/2029

#4 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

MATHEMATICA

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

KEYWORD

nonn,new

nonn

#3 by N. J. A. Sloane at Tue Jan 24 03:00:00 EST 2006

KEYWORD

nonn,new

nonn

AUTHOR

Labos E. (labos(AT)ana1ana.sote.hu), Oct 28 2003

#2 by N. J. A. Sloane at Sat Jun 12 03:00:00 EDT 2004

CROSSREFS

Cf. A016754, A088827-A088828; , A088830.

KEYWORD

nonn,new

nonn

#1 by N. J. A. Sloane at Thu Feb 19 03:00:00 EST 2004

NAME

Even numbers with even abundance.

DATA

6, 10, 12, 14, 20, 22, 24, 26, 28, 30, 34, 38, 40, 42, 44, 46, 48, 52, 54, 56, 58, 60, 62, 66, 68, 70, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 130, 132, 134, 136, 138, 140, 142, 146, 148, 150, 152

OFFSET

1,1

COMMENTS

Odd numbers with odd abundance are in A016754. Odd numbers with even abundance are in A088828. Even numbers with odd abundance are in A088827.

EXAMPLE

Even perfect numbers are here.

n=10: sigma[10]=18, abundance=18-20=-2<0;

n=12: sigma[12]=28, abundance=28-24=+4>0.

sigma[n] is also even number; sign of abundance:<=>0.

MATHEMATICA

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

CROSSREFS

Cf. A016754, A088827-A088828; A088830.

KEYWORD

nonn

AUTHOR

Labos E. (labos(AT)ana1.sote.hu), Oct 28 2003

STATUS

approved