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A139306
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Ultraperfect numbers: 2^(2p - 1), where p is A000043(n).
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23
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8, 32, 512, 8192, 33554432, 8589934592, 137438953472, 2305843009213693952, 2658455991569831745807614120560689152, 191561942608236107294793378393788647952342390272950272
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Sum of n-th even perfect number and n-th even superperfect number.
Also, sum of n-th perfect number and n-th superperfect number, if there are no odd perfect and odd superperfect numbers, then the n-th perfect number is the difference between a(n) and the n-th superperfect number (see A135652, A135653, A135654 and A135655).
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LINKS
| O. E. Pol, Determinacion geometrica de los numeros primos y perfectos.
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FORMULA
| a(n) = 2^(2*A000043(n) - 1). Also, a(n) = 2^A133033(n), if there are no odd perfect numbers. Also, a(n) = A000396(n) + A019279(n), if there are no odd perfect and odd superperfect numbers. Also, a(n) = A000396(n) + A061652(n), if there are no odd perfect numbers, the we can write: perfect number A000396(n) = a(n) - A061652(n).
a(n) = A061652(n)*(A000668(n)+1) = A061652(n)*A075398(n). - Omar E. Pol (info(AT)polprimos.com), Apr 13 2008
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EXAMPLE
| a(5)=33554432 because A000043(5)=13 and 2^(2*13 - 1) = 2^25 = 33554432.
Also, if there are no odd perfect and odd superperfect numbers then we can write a(5) = A000396(5) + A019279(5) = A000396(5) + A061652(5) = 33554432.
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CROSSREFS
| Cf. A000079, A000396, A019279, A061645, A061652, A133033, A135652, A135653, A135654, A135655, A139286, A139294, A139307.
Cf. A000043, A000668, A075398.
Sequence in context: A140789 A120781 A139286 * A166995 A079271 A031445
Adjacent sequences: A139303 A139304 A139305 * A139307 A139308 A139309
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KEYWORD
| nonn
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), Apr 13 2008
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EXTENSIONS
| Fixed typo in example. - Omar E. Pol (info(AT)polprimos.com), Nov 25 2008
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