A154895 Perfect numbers whose number of proper divisors is prime.

6, 28, 8128, 137438691328, 2305843008139952128

Offset

1,1

Comments

The next term is too large to include in the data section. If there are no odd perfect numbers then the next term is a(6) = 2^606 * (2^607 - 1) = 1.410... * 10^365. - Amiram Eldar, Jul 29 2020

Links

Table of n, a(n) for n=1..5.

Formula

a(n) = A006516(A172461(n)), assuming that odd perfect numbers do not exist. - Amiram Eldar, Jul 29 2020

Example

28 is member because the number of proper divisors of 28 is 5, a prime number.

Mathematica

Table[2^(p-1)*(2^p-1), {p, Select[MersennePrimeExponent[Range[8]], PrimeQ[2# - 1] &]}] (* Amiram Eldar, Jul 29 2020 *)

Crossrefs

Cf. A000396, A006516, A032741, A133033, A154896, A172461.

Sequence in context: A038182 A095723 A057246 * A330163 A276493 A074849

Adjacent sequences: A154892 A154893 A154894 * A154896 A154897 A154898

Keyword

nonn

Author

Omar E. Pol, Jan 25 2009

Status

approved