

A133033


Number of proper divisors of nth even perfect number.


13



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, 26933833, 41992021, 48073165, 51929901, 60804913
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OFFSET

1,1


COMMENTS

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 nth even perfect number written in base 2.


LINKS

Ivan Panchenko, Table of n, a(n) for n = 1..47
C. K. Caldwell, "Top Twenty" page, Mersenne Primes.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.


FORMULA

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.


CROSSREFS

Cf. A135650.
Sequence in context: A153263 A295140 A144933 * A145365 A146433 A134672
Adjacent sequences: A133030 A133031 A133032 * A133034 A133035 A133036


KEYWORD

nonn


AUTHOR

Omar E. Pol, Oct 27 2007, Feb 23 2008, Apr 28 2009


EXTENSIONS

a(39)a(43) from Ivan Panchenko, Apr 12 2018


STATUS

approved



