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

Author

N. J. A. Sloane, Nov 07 2014

Keywords

• nonn
• mult

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

Crossrefs

Cf. A000594.

Programs

Mathematica

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

PARI

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