login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A133028
Even perfect numbers divided by 2.
20
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 k such that A000203(k) is divisible 24. - Ctibor O. Zizka, Jun 29 2009
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 *)
Map[2^(#-2) * (2^# - 1) &, MersennePrimeExponent[Range[12]]] (* Amiram Eldar, Oct 21 2024 *)
CROSSREFS
Cf. A028334, A000396 (perfect numbers).
Cf. A134708, A135650. - Omar E. Pol, Jul 07 2009
Sequence in context: A081383 A351139 A001320 * A144985 A168590 A309028
KEYWORD
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