A249688 a(n) = n-th Ramanujan number A000594(n), squared.

1, 576, 63504, 2166784, 23328900, 36578304, 280361536, 7136870400, 12914731449, 13437446400, 285809990544, 137599451136, 333781196644, 161488244736, 1481478465600, 974437482496, 47691924412356, 7438885314624

Offset

1,2

Comments

For the functional equation for the Dirichlet series f(s) (for Re(s) > 12) of a(n) see the Hardy reference, p. 180, (10.14.3) or (10.14.4) with (10.14.5). It is, with Phi(s):= (2*Pi)^(-2*s)*Gamma(s)*Gamma(s-11)*Zeta(2*(s-11))*f(s), Phi(s) = Phi(23-s). - Wolfdieter Lang, Feb 09 2017

Multiplicative because A000594 is. - Andrew Howroyd, Jul 25 2018

References

G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, AMS Chelsea Publishing, Providence, Rhode Island, 2002, lecture X, p. 180.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Mathematica

Table[RamanujanTau[n]^2, {n, 18}] (* Michael De Vlieger, Feb 09 2017 *)

Prog

(PARI) a(n)=ramanujantau(n)^2 \\ Andrew Howroyd, Jul 25 2018

Crossrefs

Cf. A000594.

Sequence in context: A223301 A168660 A268903 * A079396 A299414 A300054

Adjacent sequences: A249685 A249686 A249687 * A249689 A249690 A249691

Keyword

nonn,mult

Author

N. J. A. Sloane, Nov 07 2014

Status

approved