cp's OEIS Frontend

A133028 Even perfect numbers divided by 2.

%I A133028 #30 Oct 21 2024 04:36:07
%S A133028 3,14,248,4064,16775168,4294934528,68719345664,1152921504069976064,
%T A133028 1329227995784915872327346307976921088,
%U A133028 95780971304118053647396689042151819065498660774084608,6582018229284824168619876730229361455111736159193471558891864064,7237005577332262213973186563042994240786838745737417944533177174565599576064
%N A133028 Even perfect numbers divided by 2.
%C A133028 a(13) has 314 digits and is too large to include. - _R. J. Mathar_, Oct 23 2007
%C A133028 Largest proper divisor of n-th even perfect number.
%C A133028 Also numbers k such that A000203(k) is divisible 24. - _Ctibor O. Zizka_, Jun 29 2009
%H A133028 Amiram Eldar, <a href="/A133028/b133028.txt">Table of n, a(n) for n = 1..15</a>
%H A133028 Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.
%F A133028 a(n) = A000396(n)/2. - _R. J. Mathar_, Oct 23 2007 [Assuming there are no odd perfect numbers. - _Jianing Song_, Sep 17 2022]
%F A133028 a(n) = 2^(A000043(n) - 2) * A000668(n). - _Omar E. Pol_, Mar 01 2008
%F A133028 a(n) = A032742(A000396(n)), assuming there are no odd perfect numbers.
%p A133028 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
%t A133028 p = Select[2^Range[400] - 1, PrimeQ]; p*(p+1)/4 (* _Vladimir Joseph Stephan Orlovsky_, Feb 02 2012 *)
%t A133028 Map[2^(#-2) * (2^# - 1) &, MersennePrimeExponent[Range[12]]] (* _Amiram Eldar_, Oct 21 2024 *)
%Y A133028 Cf. A028334, A000396 (perfect numbers).
%Y A133028 Cf. A000043, A000668, A000203.
%Y A133028 Cf. A018254, A018487, A032742, A133024, A133025, A135652, A135653, A135654, A135655.
%Y A133028 Cf. A134708, A135650. - _Omar E. Pol_, Jul 07 2009
%K A133028 nonn
%O A133028 1,1
%A A133028 _Omar E. Pol_, Oct 20 2007, Apr 23 2008, Apr 28 2009
%E A133028 More terms from _R. J. Mathar_ and _Emeric Deutsch_, Oct 23 2007