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

1,2

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

George E. Andrews and Bruce C. Berndt, Ramanujan's Unpublished Manuscript on the Partition and Tau Functions, in: Ramanujan's Lost Notebook, Part III, Springer, New York, NY, 2012.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.

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)

Mathematica

a[n_] := Mod[RamanujanTau[n], 2048]; Array[a, 100] (* Amiram Eldar, Jan 05 2025 *)

Prog

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

Crossrefs

Cf. A000594, A013959.

Sequence in context: A257766 A379982 A359839 * A333057 A156855 A306870

Adjacent sequences: A126818 A126819 A126820 * A126822 A126823 A126824

Keyword

nonn

Author

N. J. A. Sloane, Feb 25 2007

Status

approved