A126829 Ramanujan numbers (A000594) read mod 243.

1, 219, 9, 229, 213, 27, 23, 159, 81, 234, 12, 117, 116, 177, 216, 70, 126, 0, 38, 177, 207, 198, 69, 216, 223, 132, 0, 164, 84, 162, 98, 9, 108, 135, 39, 81, 236, 60, 72, 90, 87, 135, 203, 75, 0, 45, 75, 144, 21, 237, 162, 77, 135, 0, 126, 12, 99, 171, 24, 135, 50, 78, 162

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) == sigma_11(n) (mod 243) for n == 1 (mod 3) (Kolberg, 1962). - Amiram Eldar, Jan 05 2025

Mathematica

a[n_] := Mod[RamanujanTau[n], 243]; Array[a, 100] (* Amiram Eldar, Jan 05 2025 *)

Prog

(PARI) a(n) = ramanujantau(n) % 243; \\ Amiram Eldar, Jan 05 2025

Crossrefs

Cf. A000594, A013959.

Sequence in context: A230333 A060530 A252997 * A171406 A025406 A025404

Adjacent sequences: A126826 A126827 A126828 * A126830 A126831 A126832

Keyword

nonn,changed

Author

N. J. A. Sloane, Feb 25 2007

Status

approved