A133024 Divisors of 8128, the 4th perfect number.

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

Offset: 1

Author

Omar E. Pol, Oct 26 2007, Mar 03 2008, Dec 27 2008

Keywords

• fini
• full
• nonn
• easy

Comments

127 is the 4th Mersenne prime: A000668.

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

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

Links

• Index entries for sequences related to divisors of numbers
• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Crossrefs

Cf. A018254, A018487. Perfect numbers: A000396.

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

Programs

Mathematica

Divisors[8128] (* Harvey P. Dale, Jul 30 2023 *)

PARI

divisors(8128) \\ Charles R Greathouse IV, Jun 21 2017

Formula

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).