A126824 Ramanujan numbers (A000594) read mod 16384.

1, 16360, 252, 14912, 4830, 10336, 16024, 2560, 1045, 15152, 10324, 5888, 12086, 8640, 4744, 4096, 8114, 7688, 11820, 896, 7584, 14368, 14664, 6144, 10663, 4848, 6552, 5632, 5222, 832, 11616, 0, 12976, 1872, 14288, 1856, 9534, 11232, 14632, 11264, 2938, 14592

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) == 705 * sigma_11(n) (mod 16384) for n == 7 (mod 8) (Kolberg, 1962). - Amiram Eldar, Jan 05 2025

Mathematica

a[n_] := Mod[RamanujanTau[n], 16384]; Array[a, 100] (* Amiram Eldar, Jan 05 2025 *)

Prog

(PARI) a(n) = ramanujantau(n) % 16384; \\ Amiram Eldar, Jan 05 2025

Crossrefs

Cf. A000594, A013959.

Sequence in context: A013690 A247826 A223109 * A236778 A344102 A307493

Adjacent sequences: A126821 A126822 A126823 * A126825 A126826 A126827

Keyword

nonn

Author

N. J. A. Sloane, Feb 25 2007

Status

approved