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A134708
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Even superperfect numbers divided by 2.
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11
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1, 2, 8, 32, 2048, 32768, 131072, 536870912, 576460752303423488, 154742504910672534362390528, 40564819207303340847894502572032, 42535295865117307932921825928971026432
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(13) and a(14) have 157 and 183 digits respectively. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 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. [From Omar E. Pol (info(AT)polprimos.com), Jan 11 2009]
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LINKS
| O. E. Pol, Determinacion geometrica de los numeros primos y perfectos [From Omar E. Pol (info(AT)polprimos.com), Jan 11 2009]
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FORMULA
| a(n)=A061652(n)/2.
a(n) = 2^(A000043(n)-2). - Omar E. Pol (info(AT)polprimos.com), 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..nth superperfect number}x*(-1)^x [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 21 2009].
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EXAMPLE
| a(5)=2048 because the 5th even superperfect number is 4096 and 4096/2=2048.
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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 (mathar(AT)strw.leidenuniv.nl), Jan 07 2008
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CROSSREFS
| Cf. A019279, A061652, A133028.
Cf. A000043.
Cf. A032742, A138882, A139248.
Cf. A000217, A000396, A014635. [From Omar E. Pol (info(AT)polprimos.com), Jan 11 2009]
Sequence in context: A085466 A084039 A135620 * A037513 A037716 A099015
Adjacent sequences: A134705 A134706 A134707 * A134709 A134710 A134711
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KEYWORD
| nonn
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), Nov 07 2007, Apr 23 2008
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 07 2008
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