A126822 Ramanujan numbers (A000594) read mod 4096.

1, 4072, 252, 2624, 734, 2144, 3736, 2560, 1045, 2864, 2132, 1792, 3894, 448, 648, 0, 4018, 3592, 3628, 896, 3488, 2080, 2376, 2048, 2471, 752, 2456, 1536, 1126, 832, 3424, 0, 688, 1872, 2000, 1856, 1342, 3040, 2344, 3072, 2938, 2304, 3764, 3328, 1078, 320

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) == 1537 * sigma_11(n) (mod 4096) for n == 5 (mod 8) (Kolberg, 1962). - Amiram Eldar, Jan 05 2025

Mathematica

a[n_] := Mod[RamanujanTau[n], 4096]; Array[a, 100] (* Amiram Eldar, Jan 05 2025 *)

Prog

(PARI) a(n) = ramanujantau(n) % 4096; \\ Amiram Eldar, Jan 05 2025

Crossrefs

Cf. A000594, A013959.

Sequence in context: A013688 A221452 A233985 * A251005 A256028 A063889

Adjacent sequences: A126819 A126820 A126821 * A126823 A126824 A126825

Keyword

nonn

Author

N. J. A. Sloane, Feb 25 2007

Status

approved