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A061645
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a(n) is the number of divisors of n-th even perfect number.
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13
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4, 6, 10, 14, 26, 34, 38, 62, 122, 178, 214, 254, 1042, 1214, 2558, 4406, 4562, 6434, 8506, 8846, 19378, 19882, 22426, 39874, 43402, 46418, 88994, 172486, 221006, 264098, 432182, 1513678, 1718866, 2515574, 2796538, 5952442, 6042754, 13945186, 26933834
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OFFSET
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1,1
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COMMENTS
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The number of divisors of n-th perfect number that are powers of 2 is equal to a(n)/2, assuming there are no odd perfect numbers. The number of divisors of n-th perfect number that are multiples of n-th Mersenne prime A000668(n) is also equal to a(n)/2, assuming there are no odd perfect numbers. (See A000043). - Omar E. Pol, Feb 28 2008
The n-th even perfect number A000396(n) = 2^(p-1)*P with Mersenne prime P = 2^p-1, p = A000043(n), has obviously the 2p divisors { 1, 2, 2^2, ..., 2^(p-1) } U { P, 2*P, ..., 2^(p-1)*P }. - M. F. Hasler, Dec 10 2018
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LINKS
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FORMULA
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EXAMPLE
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8128 = 2*2*2*2*2*2*127 with 14 divisors.
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MATHEMATICA
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2 * Array[MersennePrimeExponent, 45] (* Amiram Eldar, Dec 10 2018 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Definition changed (inserting the word "even") by Ivan Panchenko, Apr 16 2018
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STATUS
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approved
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