cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A134710 a(n) = n-th even superperfect number divided by 2^n.

This page as a plain text file.
%I A134710 #20 Oct 21 2024 04:35:58
%S A134710 1,1,2,4,128,1024,2048,4194304,2251799813685248,
%T A134710 302231454903657293676544,39614081257132168796771975168,
%U A134710 20769187434139310514121985316880384
%N A134710 a(n) = n-th even superperfect number divided by 2^n.
%C A134710 a(13) and a(14) have 153 and 179 digits respectively and are too large to include here. - _R. J. Mathar_, Jan 07 2008
%H A134710 Amiram Eldar, <a href="/A134710/b134710.txt">Table of n, a(n) for n = 1..18</a>
%H A134710 Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.
%F A134710 a(n) = A061652(n)/(2^n).
%F A134710 a(n) = 2^(A000043(n)-n-1). - _Amiram Eldar_, Oct 21 2024
%e A134710 a(5) = 128 because the 5th even superperfect number is 4096 and 2^5 = 32 and 4096/32 = 128.
%p A134710 A000043 := proc(n) op(n,[2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213]) ; end: A061652 := proc(n) 2^(A000043(n)-1) ; end: A134710 := proc(n) A061652(n)/2^n ; end: seq(A134710(n),n=1..14) ; # _R. J. Mathar_, Jan 07 2008
%t A134710 With[{max = 12}, 2^(MersennePrimeExponent[Range[max]] - Range[max] - 1)] (* _Amiram Eldar_, Oct 21 2024 *)
%Y A134710 Cf. A000043, A000396, A000668, A019279, A061652 (even superperfect numbers), A133028.
%K A134710 nonn
%O A134710 1,3
%A A134710 _Omar E. Pol_, Nov 07 2007
%E A134710 More terms from _R. J. Mathar_, Jan 07 2008