A134708 Even superperfect numbers divided by 2.

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

Offset

1,2

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

Links

Table of n, a(n) for n=1..12.

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos [From Omar E. Pol, Jan 11 2009]

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

Example

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

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

Crossrefs

Cf. A019279, A061652, A133028.

Cf. A000043.

Cf. A032742, A138882, A139248.

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

Sequence in context: A085466 A084039 A135620 * A294530 A037513 A037716

Adjacent sequences: A134705 A134706 A134707 * A134709 A134710 A134711

Keyword

nonn

Author

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

Extensions

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

Status

approved