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

%I A096060 #34 Sep 08 2022 08:45:14
%S A096060 1,3,31,105,1285,4599,60787,3085465,11545611,619094385,8939118925,
%T A096060 34093383807,499069107643,28324525958305,1628420204246959,
%U A096060 6300117511512825,367099384551433863,5542683665339959171
%N A096060 (2^(p-1)-1)/(3*p) where p = prime(n).
%H A096060 T. D. Noe, <a href="/A096060/b096060.txt">Table of n, a(n) for n=3..100</a>
%H A096060 P. Terzich, <a href="http://vixra.org/abs/1202.0024">On the Form of Mersenne Numbers</a>, vixra:1202.0024. - From _N. J. A. Sloane_, Jun 20 2012
%F A096060 a(n) = A001045(prime(n)-1)/prime(n).
%F A096060 a(n) = A007663(n)/3 for n>2. - _Alexander Adamchuk_, Jun 08 2006
%F A096060 a(n) = A002450((p-1)/2)/p, for p=prime(n) and n>=3. - _Roderick MacPhee_, Sep 29 2014
%p A096060 seq((2^(ithprime(n)-1)-1)/(3*ithprime(n)), n=3..50); # _Robert Israel_, Oct 14 2014
%t A096060 Table[(2^(Prime[n]-1)-1)/(3*Prime[n]),{n,3,22}] (* _Alexander Adamchuk_, Jun 08 2006 *)
%t A096060 Table[(2^(n-1)-1)/(3n),{n,Prime[Range[3,20]]}] (* _Harvey P. Dale_, Dec 27 2014 *)
%o A096060 (PARI) b(n) = (4^n - 1)/3;
%o A096060 a(n) = p = prime(n); b((p-1)/2)/p; \\ _Michel Marcus_, Sep 30 2014
%o A096060 (Magma)  [(2^(NthPrime(n)-1)-1) div (3*NthPrime(n)): n in [3..25]]; // _Vincenzo Librandi_, Oct 15 2014
%Y A096060 Cf. A001045, A002450, A007663.
%K A096060 nonn
%O A096060 3,2
%A A096060 _Amarnath Murthy_, Jun 18 2004
%E A096060 More terms from _Alexander Adamchuk_, Jun 08 2006
%E A096060 Formula using A001045 corrected by _Jonathan Sondow_, Jul 19 2010