

A249688


a(n) = nth Ramanujan number A000594(n), squared.


1



1, 576, 63504, 2166784, 23328900, 36578304, 280361536, 7136870400, 12914731449, 13437446400, 285809990544, 137599451136, 333781196644, 161488244736, 1481478465600, 974437482496, 47691924412356, 7438885314624
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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(s11)*Zeta(2*(s11))*f(s), Phi(s) = Phi(23s).  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



