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A133028
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Even perfect numbers divided by 2.
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16
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3, 14, 248, 4064, 16775168, 4294934528, 68719345664, 1152921504069976064, 1329227995784915872327346307976921088, 95780971304118053647396689042151819065498660774084608, 6582018229284824168619876730229361455111736159193471558891864064, 7237005577332262213973186563042994240786838745737417944533177174565599576064
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(13) has 314 digits and is too large to include. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 23 2007
Largest proper divisor of n-th even perfect number.
Also numbers n such that A000203(n) is divisible 24. [From Ctibor O. Zizka (c.zizka(AT)email.cz), Jun 29 2009]
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LINKS
| O. E. Pol, Determinacion geometrica de los numeros primos y perfectos.
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FORMULA
| a(n)=A000396(n)/2. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 23 2007
a(n) = 2^(A000043(n)-2) * A000668(n). - Omar E. Pol (info(AT)polprimos.com), Mar 01 2008
a(n) = A032742(A000396(n)), assuming there are no odd perfect numbers.
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MAPLE
| a:=proc(n) if isprime(2^n-1)=true then 2^(n-2)*(2^n-1) else end if end proc: seq(a(n), n=1..120); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 24 2007
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MATHEMATICA
| p = Select[2^Range[400] - 1, PrimeQ]; p*(p+1)/4 (* From Vladimir Joseph Stephan Orlovsky, Feb 02 2012 *)
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CROSSREFS
| Cf. A028334. Perfect numbers: A000396.
Cf. A000043, A000668.
Cf. A018254, A018487, A032742, A133024, A133025, A135652, A135653, A135654, A135655.
Cf. A134708, A135650. [From Omar E. Pol (info(AT)polprimos.com), Jul 07 2009]
Sequence in context: A058388 A081383 A001320 * A144985 A168590 A081397
Adjacent sequences: A133025 A133026 A133027 * A133029 A133030 A133031
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KEYWORD
| easy,nonn,changed
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), Oct 20 2007, Apr 23 2008, Apr 28 2009
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 23 2007
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