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

1,2

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.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000594, A013959.

Sequence in context: A109145 A226001 A096329 * A205092 A014885 A252217

Adjacent sequences: A126820 A126821 A126822 * A126824 A126825 A126826

Keyword

nonn

Author

N. J. A. Sloane, Feb 25 2007

Status

approved