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

1, 1, 2, 4, 128, 1024, 2048, 4194304, 2251799813685248, 302231454903657293676544, 39614081257132168796771975168, 20769187434139310514121985316880384

Offset: 1

Author

Omar E. Pol, Nov 07 2007

Keywords

• nonn

Comments

a(13) and a(14) have 153 and 179 digits respectively and are too large to include here. - R. J. Mathar, Jan 07 2008

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..18
• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Crossrefs

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

Programs

Maple

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

Mathematica

With[{max = 12}, 2^(MersennePrimeExponent[Range[max]] - Range[max] - 1)] (* Amiram Eldar, Oct 21 2024 *)

Formula

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

a(n) = 2^(A000043(n)-n-1). - Amiram Eldar, Oct 21 2024

Extensions

More terms from R. J. Mathar, Jan 07 2008