A133202 - OEIS

%I #29 Jan 19 2025 00:35:50

%S 1,8,18,14,32,48,32,80,20,120,48,108,16,112,192,26,48,96,144,192,216,

%T 144,32,384,12,80,224,120,32,420,72,192,320,160,360,210,8,576,144,792,

%U 32,432,12,216,288,84,40,180,12,96,240,128,32,448,576,832,960,120

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

%H Amiram Eldar, <a href="/A133202/b133202.txt">Table of n, a(n) for n = 1..10000</a>

%H Bruce C. Berndt and Ken Ono, <a href="http://www.emis.de/journals/SLC/wpapers/s42berndt.html">Ramanujan's unpublished manuscript on the partition and tau functions with proofs and commentary</a>, Séminaire Lotharingien de Combinatoire, B42c (1999), 63 pp.

%H Stephen C. Milne, <a href="http://www.pnas.org/cgi/reprint/93/26/15004.pdf">New infinite families of exact sums of squares formulas, Jacobi elliptic functions and Ramanujan's tau function</a>, Proc. Natl. Acad. Sci. USA, 93 (1996), pp. 15004-15008.

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

%t Table[DivisorSigma[0, RamanujanTau[n]], {n, 100}] (* _T. D. Noe_, Aug 22 2011 *)

%o (Perl) use ntheory ":all"; say scalar(divisors(abs(ramanujan_tau($_)))) for 1..100; # _Dana Jacobsen_, Sep 05 2015

%o (PARI) a(n)=numdiv(abs(ramanujantau(n))) \\ _Charles R Greathouse IV_, Feb 08 2017

%Y Cf. A000005, A000594.

%K nonn

%O 1,2

%A _Ctibor O. Zizka_, Dec 18 2007

%E Corrected and extended by _Carl Najafi_, Aug 21 2011