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Divisors of 8128, the 4th perfect number.
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%I #14 Jul 30 2023 14:11:18

%S 1,2,4,8,16,32,64,127,254,508,1016,2032,4064,8128

%N Divisors of 8128, the 4th perfect number.

%C 127 is the 4th Mersenne prime: A000668.

%C The number of divisors of the 4th perfect number is 2*A000043(4)=A061645(4)=14.

%C For the structure of this sequence and its binary expansion, see A135654.

%H <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>

%H Omar E. Pol, <a href="http://www.polrpimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.

%F For n=1..7 : a(n) = 2^(n-1). For n=8..14: a(n) = 2^(n-1) - 2^(n-8) = A000668(4)*2^(n-8).

%t Divisors[8128] (* _Harvey P. Dale_, Jul 30 2023 *)

%o (PARI) divisors(8128) \\ _Charles R Greathouse IV_, Jun 21 2017

%Y Cf. A018254, A018487. Perfect numbers: A000396.

%Y Cf. A000079, A000668, A061645, A133033, A135654.

%K fini,full,nonn,easy

%O 1,2

%A _Omar E. Pol_, Oct 26 2007, Mar 03 2008, Dec 27 2008