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A061645
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a(n) = number of divisors of n-th perfect number.
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12
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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
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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
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LINKS
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Table of n, a(n) for n=1..37.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.
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FORMULA
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a(n) = A000005[A000396(n)] = 2*A000043(n)
a(n) = floor{log_2(A000396(n))} + 2. - Lekraj Beedassy, Aug 21 2004
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EXAMPLE
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8128 = 2*2*2*2*2*2*127 with 14 divisors.
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CROSSREFS
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Cf. A000005, A000396, A000043.
Cf. A000668.
Sequence in context: A061227 A000066 A241160 * A188592 A188586 A084372
Adjacent sequences: A061642 A061643 A061644 * A061646 A061647 A061648
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KEYWORD
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easy,nonn
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AUTHOR
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Labos Elemer, Jun 14 2001
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STATUS
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approved
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