A133028 Even perfect numbers divided by 2.

3, 14, 248, 4064, 16775168, 4294934528, 68719345664, 1152921504069976064, 1329227995784915872327346307976921088, 95780971304118053647396689042151819065498660774084608, 6582018229284824168619876730229361455111736159193471558891864064, 7237005577332262213973186563042994240786838745737417944533177174565599576064

Offset

1,1

Comments

a(13) has 314 digits and is too large to include. - R. J. Mathar, Oct 23 2007

Largest proper divisor of n-th even perfect number.

Also numbers n such that A000203(n) is divisible 24. - Ctibor O. Zizka, Jun 29 2009

Links

Table of n, a(n) for n=1..12.

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Formula

a(n) = A000396(n)/2. - R. J. Mathar, Oct 23 2007 [Assuming there are no odd perfect numbers. - Jianing Song, Sep 17 2022]

a(n) = 2^(A000043(n) - 2) * A000668(n). - Omar E. Pol, Mar 01 2008

a(n) = A032742(A000396(n)), assuming there are no odd perfect numbers.

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, Oct 24 2007

Mathematica

p = Select[2^Range[400] - 1, PrimeQ]; p*(p+1)/4 (* Vladimir Joseph Stephan Orlovsky, Feb 02 2012 *)

Crossrefs

Cf. A028334. Perfect numbers: A000396.

Cf. A000043, A000668.

Cf. A018254, A018487, A032742, A133024, A133025, A135652, A135653, A135654, A135655.

Cf. A134708, A135650. - Omar E. Pol, Jul 07 2009

Sequence in context: A081383 A351139 A001320 * A144985 A168590 A309028

Adjacent sequences: A133025 A133026 A133027 * A133029 A133030 A133031

Keyword

easy,nonn

Author

Omar E. Pol, Oct 20 2007, Apr 23 2008, Apr 28 2009

Extensions

More terms from R. J. Mathar and Emeric Deutsch, Oct 23 2007

Status

approved