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A134708
Even superperfect numbers divided by 2.
11
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
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
MATHEMATICA
With[{max = 12}, 2^(MersennePrimeExponent[Range[max]] - 2)] (* Amiram Eldar, Oct 21 2024 *)
CROSSREFS
Cf. A000043.
Cf. A000217, A000396, A014635. - Omar E. Pol, Jan 11 2009
Sequence in context: A085466 A084039 A135620 * A294530 A037513 A037716
KEYWORD
nonn
AUTHOR
Omar E. Pol, Nov 07 2007, Apr 23 2008
EXTENSIONS
More terms from R. J. Mathar, Jan 07 2008
STATUS
approved