%I #10 Jan 05 2025 01:07:56
%S 1,3,9,13,24,0,23,24,0,18,12,9,8,15,0,16,18,0,11,15,18,9,15,0,7,24,0,
%T 2,3,0,17,9,0,0,12,0,20,6,18,9,6,0,14,21,0,18,21,9,21,21,0,23,0,0,18,
%U 12,18,9,24,0,23,24,0,10,3,0,8,18,0,9,18,0,11,6,9,8,6,0,5,6,0,18,3,18,0,15,0
%N Ramanujan numbers (A000594) read mod 27.
%H Amiram Eldar, <a href="/A126827/b126827.txt">Table of n, a(n) for n = 1..10000</a>
%H George E. Andrews and Bruce C. Berndt, <a href="https://doi.org/10.1007/978-1-4614-3810-6_5">Ramanujan's Unpublished Manuscript on the Partition and Tau Functions</a>, in: Ramanujan's Lost Notebook, Part III, Springer, New York, NY, 2012.
%H R. P. Bambah and S. Chowla, <a href="http://dx.doi.org/10.1090/S0002-9904-1947-08913-8">Congruence properties of Ramanujan’s function tau(n)</a>, Bull. Amer. Math. Soc., Vol. 53 (1947), pp. 950-955.
%H H. P. F. Swinnerton-Dyer, <a href="http://dx.doi.org/10.1007/978-3-540-37802-0_1">On l-adic representations and congruences for coefficients of modular forms</a>, pp. 1-55 of Modular Functions of One Variable III (Antwerp 1972), Lect. Notes Math., 350, 1973.
%F a(n) == n^2 * sigma_7(n) (mod 27) (Bambah and Chowla, 1947, eq. (16), p. 954; Andrews and Berndt, 2012, eq. (5.12.3), p. 114). - _Amiram Eldar_, Jan 05 2025
%t a[n_] := Mod[RamanujanTau[n], 27]; Array[a, 100] (* _Amiram Eldar_, Jan 05 2025 *)
%o (PARI) a(n) = ramanujantau(n) % 27; \\ _Amiram Eldar_, Jan 05 2025
%Y Cf. A000594, A013955.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Feb 25 2007