A126823 Ramanujan numbers (A000594) read mod 8192.

1, 8168, 252, 6720, 4830, 2144, 7832, 2560, 1045, 6960, 2132, 5888, 3894, 448, 4744, 4096, 8114, 7688, 3628, 896, 7584, 6176, 6472, 6144, 2471, 4848, 6552, 5632, 5222, 832, 3424, 0, 4784, 1872, 6096, 1856, 1342, 3040, 6440, 3072, 2938, 6400, 3764, 7424, 1078

Offset: 1

Author

N. J. A. Sloane, Feb 25 2007

Keywords

• nonn

References

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• H. P. F. Swinnerton-Dyer, On l-adic representations and congruences for coefficients of modular forms, pp. 1-55 of Modular Functions of One Variable III (Antwerp 1972), Lect. Notes Math., 350, 1973.

Crossrefs

Cf. A000594, A013959.

Programs

Mathematica

a[n_] := Mod[RamanujanTau[n], 8192]; Array[a, 100] (* Amiram Eldar, Jan 05 2025 *)

PARI

a(n) = ramanujantau(n) % 8192; \\ Amiram Eldar, Jan 05 2025

Formula

a(n) == 1217 * sigma_11(n) (mod 8192) for n == 3 (mod 8) (Kolberg, 1962). - Amiram Eldar, Jan 05 2025