A133202 Number of divisors of the absolute value of Ramanujan tau numbers. a(n) = 0 if tau(n) = 0.

1, 8, 18, 14, 32, 48, 32, 80, 20, 120, 48, 108, 16, 112, 192, 26, 48, 96, 144, 192, 216, 144, 32, 384, 12, 80, 224, 120, 32, 420, 72, 192, 320, 160, 360, 210, 8, 576, 144, 792, 32, 432, 12, 216, 288, 84, 40, 180, 12, 96, 240, 128, 32, 448, 576, 832, 960, 120

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Bruce C. Berndt and Ken Ono, Ramanujan's unpublished manuscript on the partition and tau functions with proofs and commentary, Séminaire Lotharingien de Combinatoire, B42c (1999), 63 pp.

Stephen C. Milne, New infinite families of exact sums of squares formulas, Jacobi elliptic functions and Ramanujan's tau function, Proc. Natl. Acad. Sci. USA, 93 (1996), pp. 15004-15008.

Formula

a(n) = A000005(abs(A000594(n))).

Mathematica

Table[DivisorSigma[0, RamanujanTau[n]], {n, 100}] (* T. D. Noe, Aug 22 2011 *)

Prog

(Perl) use ntheory ":all"; say scalar(divisors(abs(ramanujan_tau($_)))) for 1..100; # Dana Jacobsen, Sep 05 2015
(PARI) a(n)=numdiv(abs(ramanujantau(n))) \\ Charles R Greathouse IV, Feb 08 2017

Crossrefs

Cf. A000005, A000594.

Sequence in context: A137788 A378228 A333828 * A217424 A332969 A322031

Adjacent sequences: A133199 A133200 A133201 * A133203 A133204 A133205

Keyword

nonn

Author

Ctibor O. Zizka, Dec 18 2007

Extensions

Corrected and extended by Carl Najafi, Aug 21 2011

Status

approved