A090748 - OEIS

A090748

Numbers n such that 2^(n+1) - 1 is prime.

1, 2, 4, 6, 12, 16, 18, 30, 60, 88, 106, 126, 520, 606, 1278, 2202, 2280, 3216, 4252, 4422, 9688, 9940, 11212, 19936, 21700, 23208, 44496, 86242, 110502, 132048, 216090, 756838, 859432, 1257786, 1398268, 2976220, 3021376, 6972592, 13466916, 20996010, 24036582, 25964950, 30402456, 32582656

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OFFSET

1,2

COMMENTS

Perfect numbers A000396(n) = 2^A133033(n) - 2^a(n), assuming there are no odd perfect numbers. - Omar E. Pol, Feb 24 2008

Number of proper divisors of n-th even perfect number that are multiples of n-th Mersenne prime A000668(n). - Omar E. Pol, Feb 28 2008

Base 2 logarithm of n-th even superperfect number A061652(n). Also base 2 logarithm of n-th superperfect number A019279(n), assuming there are no odd superperfect numbers. - Omar E. Pol, Apr 11 2008

Number of 0's in binary expansion of n-th even perfect number (see A135650). - Omar E. Pol, May 04 2008

LINKS

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

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

FORMULA

2^a(n) = A051027(2^(n+1)). - Juri-Stepan Gerasimov, Aug 21 2016

EXAMPLE

1 is in the sequence because 2^2 - 1 = 3 is prime.

MATHEMATICA

Select[Range[0, 10^4], PrimeQ[2^(# + 1) - 1] &] (* Vincenzo Librandi, Jul 28 2016 *)

PROG

(Magma) [n: n in [1..5*10^3] |IsPrime(2^(n+1)-1)]; // Vincenzo Librandi, Jul 28 2016