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Search: id:A133033
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| A133033 |
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Number of proper divisors of n-th even perfect number. |
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+0
12
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| 3, 5, 9, 13, 25, 33, 37, 61, 121, 177, 213, 253, 1041, 1213, 2557, 4405, 4561, 6433, 8505, 8845, 19377, 19881, 22425, 39873, 43401, 46417, 88993, 172485, 221005, 264097, 432181, 1513677, 1718865, 2515573, 2796537, 5952441, 6042753, 13945185
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OFFSET
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1,1
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COMMENT
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Perfect numbers: A000396(n) = 2^a(n) - 2^A090748(n), assuming there are no odd perfect numbers.
Also, a(n) is equal to the number of bits in A135650(n), the n-th even perfect number written in base 2.
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LINKS
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C. K. Caldwell, "Top Twenty" page, Mersenne Primes.
O. E. Pol, Determinacion geometrica de los numeros primos y perfectos.
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FORMULA
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a(n) = A061645(n) - 1, assuming there are no odd perfect numbers.
a(n) = A000043(n) + A090748(n) = 2*A000043(n) - 1 = 2*A090748(n) + 1.
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CROSSREFS
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Cf. A135650.
Adjacent sequences: A133030 A133031 A133032 this_sequence A133034 A133035 A133036
Sequence in context: A052282 A001993 A153263 this_sequence A145365 A146433 A134672
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KEYWORD
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nonn
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AUTHOR
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Omar E. Pol (info(AT)polprimos.com), Oct 27 2007, Feb 23 2008, Apr 28 2009
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