A133049 Squares of Mersenne primes A000668(n).

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

Offset: 1

Author

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

Keywords

• nonn

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.

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..15
• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Crossrefs

Cf. A000290, A001248. Mersenne primes: A000668.

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

Programs

Mathematica

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

PARI

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

Formula

a(n) = A000668(n)^2

Extensions

More terms from Olaf Voß, Feb 13 2008