A096060 (2^(p-1)-1)/(3*p) where p = prime(n).

1, 3, 31, 105, 1285, 4599, 60787, 3085465, 11545611, 619094385, 8939118925, 34093383807, 499069107643, 28324525958305, 1628420204246959, 6300117511512825, 367099384551433863, 5542683665339959171

Offset: 3

Author

Amarnath Murthy, Jun 18 2004

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n=3..100
• P. Terzich, On the Form of Mersenne Numbers, vixra:1202.0024. - From _N. J. A. Sloane_, Jun 20 2012

Crossrefs

Cf. A001045, A002450, A007663.

Programs

Magma

[(2^(NthPrime(n)-1)-1) div (3*NthPrime(n)): n in [3..25]]; // Vincenzo Librandi, Oct 15 2014

Maple

seq((2^(ithprime(n)-1)-1)/(3*ithprime(n)), n=3..50); # Robert Israel, Oct 14 2014

Mathematica

Table[(2^(Prime[n]-1)-1)/(3*Prime[n]),{n,3,22}] (* Alexander Adamchuk, Jun 08 2006 *)
Table[(2^(n-1)-1)/(3n),{n,Prime[Range[3,20]]}] (* Harvey P. Dale, Dec 27 2014 *)

PARI

b(n) = (4^n - 1)/3;
a(n) = p = prime(n); b((p-1)/2)/p; \\ Michel Marcus, Sep 30 2014

Formula

a(n) = A001045(prime(n)-1)/prime(n).

a(n) = A007663(n)/3 for n>2. - Alexander Adamchuk, Jun 08 2006

a(n) = A002450((p-1)/2)/p, for p=prime(n) and n>=3. - Roderick MacPhee, Sep 29 2014

Extensions

More terms from Alexander Adamchuk, Jun 08 2006

Formula using A001045 corrected by Jonathan Sondow, Jul 19 2010