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”).
%I #19 Mar 16 2022 03:19:48
%S 4,16,256,4096,16777216,4294967296,68719476736,1152921504606846976,
%T 1329227995784915872903807060280344576,
%U 95780971304118053647396689196894323976171195136475136,6582018229284824168619876730229402019930943462534319453394436096
%N a(n) = 2^(2p-1)/2, where p is A000043(n).
%C Ultraperfect numbers (A139306), divided by 2.
%C Also, a(n) is the largest proper divisor of the n-th ultraperfect number.
%C The cototient (A051953) of the even perfect numbers (A000396). - _Amiram Eldar_, Mar 06 2022
%C These cototients are squares = (2^(p-1))^2. - _Bernard Schott_, Mar 14 2022
%F a(n) = A139306(n)/2.
%F a(n) = A051953(A000396(n)), if there are no odd perfect numbers. - _Amiram Eldar_, Mar 06 2022
%F a(n) = A061652(n)^2. - _Bernard Schott_, Mar 14 2022
%t a[n_] := 4^(MersennePrimeExponent[n] - 1); Array[a, 12] (* _Amiram Eldar_, Mar 06 2022 *)
%Y Cf. A000043, A000396, A019279, A051953, A061652, A139288, A139306, A152922, A152923.
%K nonn
%O 1,1
%A _Omar E. Pol_, Dec 15 2008
%E More terms from _Amiram Eldar_, Mar 06 2022