A060286 a(n) = 2^(p-1)*(2^p-1) where p is prime(n).

6, 28, 496, 8128, 2096128, 33550336, 8589869056, 137438691328, 35184367894528, 144115187807420416, 2305843008139952128, 9444732965670570950656, 2417851639228158837784576, 38685626227663735544086528, 9903520314282971830448816128, 40564819207303336344294875201536

Offset: 1

Author

Jason Earls, Mar 23 2001

Keywords

• nonn

Comments

a(n) is the number whose binary representation is p 1's together with p-1 0's, where p is prime(n), for example: prime(3) = 5 so a(3) = 496 = 111110000 (2). - Omar E. Pol, Dec 12 2012

Examples

			a(4) = 2^6(2^7 - 1) = 8128.
		

References

• C. Stanley Ogilvy and John T. Anderson, "Excursions in Number Theory", Oxford University Press, NY, 1966 pp. 20-23.

Links

• Harry J. Smith, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000040, A000396, A006516.

Programs

Mathematica

Table[2^(Prime[n] - 1)(2^Prime[n] - 1), {n, 16}] (* Alonso del Arte, Dec 12 2012 *)

PARI

{ n=0; forprime (p=1, 542, write("b060286.txt", n++, " ", 2^(p - 1)*(2^p - 1)); ) } \\ Harry J. Smith, Jul 03 2009

Formula

For n > 1, a(2n) = 9*T(k) + 1 ; a(2n+1) = 9*T(K) + 1, where T(n) = A000217(n), k = (A121290(n) - 1)/2, K = 2*A121290(n). - Lekraj Beedassy, Sep 12 2006

a(A016027(n)) = A000396(n), assuming there are no odd perfect numbers. - Omar E. Pol, Dec 13 2012