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a(n) = n-th even superperfect number divided by 2^n.
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%I #20 Oct 21 2024 04:35:58

%S 1,1,2,4,128,1024,2048,4194304,2251799813685248,

%T 302231454903657293676544,39614081257132168796771975168,

%U 20769187434139310514121985316880384

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

%C 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 Amiram Eldar, <a href="/A134710/b134710.txt">Table of n, a(n) for n = 1..18</a>

%H Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.

%F a(n) = A061652(n)/(2^n).

%F a(n) = 2^(A000043(n)-n-1). - _Amiram Eldar_, Oct 21 2024

%e a(5) = 128 because the 5th even superperfect number is 4096 and 2^5 = 32 and 4096/32 = 128.

%p 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 With[{max = 12}, 2^(MersennePrimeExponent[Range[max]] - Range[max] - 1)] (* _Amiram Eldar_, Oct 21 2024 *)

%Y Cf. A000043, A000396, A000668, A019279, A061652 (even superperfect numbers), A133028.

%K nonn,changed

%O 1,3

%A _Omar E. Pol_, Nov 07 2007

%E More terms from _R. J. Mathar_, Jan 07 2008