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A061645 a(n) = number of divisors of n-th even perfect number. 13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Ivan Panchenko, Table of n, a(n) for n = 1..47

Omar E. Pol, Los nĂºmeros perfectos, (in Spanish).

FORMULA

a(n) = A000005(A000396(n)).

a(n) = floor{log_2(A000396(n))} + 2. - Lekraj Beedassy, Aug 21 2004

EXAMPLE

8128 = 2*2*2*2*2*2*127 with 14 divisors.

CROSSREFS

Cf. A000005, A000396, A000043.

Cf. A000668.

Sequence in context: A000066 A266730 A241160 * A188592 A188586 A084372

Adjacent sequences:  A061642 A061643 A061644 * A061646 A061647 A061648

KEYWORD

nonn

AUTHOR

Labos Elemer, Jun 14 2001

EXTENSIONS

Definition changed (inserting the word "even") by Ivan Panchenko, Apr 16 2018

a(38)-a(39) from Ivan Panchenko, Apr 16 2018

STATUS

approved

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Last modified May 25 16:37 EDT 2018. Contains 304567 sequences. (Running on oeis4.)