A126821 - OEIS

%I #12 Jan 05 2025 01:09:44

%S 1,2024,252,576,734,96,1688,512,1045,816,84,1792,1846,448,648,0,1970,

%T 1544,1580,896,1440,32,328,0,423,752,408,1536,1126,832,1376,0,688,

%U 1872,2000,1856,1342,992,296,1024,890,256,1716,1280,1078,320,1808,0,1449,88,824,384

%N Ramanujan numbers (A000594) read mod 2048.

%D Oddmund Kolberg, Congruences for Ramanujan's Function ̈tau(n), Univ. Bergen Årbok Naturvit Rekke, No. 11, 1962.

%H Amiram Eldar, <a href="/A126821/b126821.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Ramanujan's Unpublished Manuscript on the Partition and Tau Functions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 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 From _Amiram Eldar_, Jan 05 2025: (Start)

%F a(n) == sigma_11(n) (mod 2048) for n == 1 (mod 8) (Kolberg, 1962).

%F a(n) == 24 * sigma_11(n) (mod 2048) (Andrews and Berndt, 2012, p. 118). (End)

%t a[n_] := Mod[RamanujanTau[n], 2048]; Array[a, 100] (* _Amiram Eldar_, Jan 05 2025 *)

%o (PARI) a(n) = ramanujantau(n) % 2048; \\ _Amiram Eldar_, Jan 05 2025

%Y Cf. A000594, A013959.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Feb 25 2007