A134708 Even superperfect numbers divided by 2.

1, 2, 8, 32, 2048, 32768, 131072, 536870912, 576460752303423488, 154742504910672534362390528, 40564819207303340847894502572032, 42535295865117307932921825928971026432

Offset: 1

Author

Omar E. Pol, Nov 07 2007, Apr 23 2008

Keywords

• nonn

Comments

a(13) and a(14) have 157 and 183 digits respectively. - R. J. Mathar, Jan 07 2008

Largest proper divisor of n-th even superperfect number A061652(n). Also, largest proper divisor of n-th superperfect number A019279(n), if there are no odd superperfect numbers.

Indices of even hexagonal numbers (A014635) that are also even perfect numbers. - Omar E. Pol, Jan 11 2009

Examples

			a(5) = 2048 because the 5th even superperfect number is 4096 and 4096/2 = 2048.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..18
• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos [From _Omar E. Pol_, Jan 11 2009]

Crossrefs

Cf. A019279, A061652, A133028.

Cf. A000043.

Cf. A032742, A138882, A139248.

Cf. A000217, A000396, A014635. - Omar E. Pol, Jan 11 2009

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: A134708 := proc(n) A061652(n)/2 ; end: seq(A134708(n),n=1..14) ; # R. J. Mathar, Jan 07 2008

Mathematica

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

Formula

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

a(n) = 2^(A000043(n)-2). - Omar E. Pol, Mar 01 2008

a(n) = A032742(A061652(n)). Also, a(n) = A032742(A019279(n)), if there are no odd superperfect numbers.

a(n) = Sum_{x=1..n-th superperfect number} x*(-1)^x. - Juri-Stepan Gerasimov, Jul 21 2009

Extensions

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