A126821 Ramanujan numbers (A000594) read mod 2048.

1, 2024, 252, 576, 734, 96, 1688, 512, 1045, 816, 84, 1792, 1846, 448, 648, 0, 1970, 1544, 1580, 896, 1440, 32, 328, 0, 423, 752, 408, 1536, 1126, 832, 1376, 0, 688, 1872, 2000, 1856, 1342, 992, 296, 1024, 890, 256, 1716, 1280, 1078, 320, 1808, 0, 1449, 88, 824, 384

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
• George E. Andrews and Bruce C. Berndt, Ramanujan's Unpublished Manuscript on the Partition and Tau Functions, in: Ramanujan's Lost Notebook, Part III, Springer, New York, NY, 2012.
• 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], 2048]; Array[a, 100] (* Amiram Eldar, Jan 05 2025 *)

PARI

a(n) = ramanujantau(n) % 2048; \\ Amiram Eldar, Jan 05 2025

Formula

From Amiram Eldar, Jan 05 2025: (Start)

a(n) == sigma_11(n) (mod 2048) for n == 1 (mod 8) (Kolberg, 1962).

a(n) == 24 * sigma_11(n) (mod 2048) (Andrews and Berndt, 2012, p. 118). (End)