A133049 Squares of Mersenne primes A000668(n).

9, 49, 961, 16129, 67092481, 17179607041, 274876858369, 4611686014132420609, 5316911983139663487003542222693990401, 383123885216472214589586755549637256619304505646776321

Offset

1,1

Comments

Sum of last A000043(n) divisors of the n-th even perfect number. In other words; sum of divisors that are not powers of 2 of the n-th even perfect number, or sum of divisors that are multiples of the n-th Mersenne prime A000668(n) of the n-th even perfect number. See A139247 for more information.

See the structure of the divisors of perfect numbers in A135652, A135653, A135654 and A135655.

Links

G. C. Greubel, Table of n, a(n) for n = 1..15

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

Formula

a(n) = A000668(n)^2

Example

a(3)=961 because the 3rd Mersenne prime is 31 and 31^2=961.

Mathematica

Select[2^Range[1000] - 1, PrimeQ]^2 (* G. C. Greubel, Oct 03 2017 *)

Prog

(PARI) forprime(p=2, 1000, if(ispseudoprime(2^p-1), print1((2^p-1)^2", "))) \\ G. C. Greubel, Oct 03 2017

Crossrefs

Cf. A000290, A001248. Mersenne primes: A000668.

Cf. A000043, A000396, A135652, A135653, A135654, A135655, A138247.

Sequence in context: A069666 A175734 A174744 * A188140 A050632 A050638

Adjacent sequences: A133046 A133047 A133048 * A133050 A133051 A133052

Keyword

nonn

Author

Omar E. Pol, Oct 30 2007, Apr 23 2008

Extensions

More terms from Olaf Voß, Feb 13 2008

Status

approved