A126830 Ramanujan numbers (A000594) read mod 729.

1, 705, 252, 715, 456, 513, 23, 645, 81, 720, 255, 117, 359, 177, 459, 70, 612, 243, 524, 177, 693, 441, 555, 702, 466, 132, 0, 407, 570, 648, 584, 495, 108, 621, 282, 324, 236, 546, 72, 333, 573, 135, 689, 75, 486, 531, 75, 144, 264, 480, 405, 77, 135, 0, 369, 255

Offset

1,2

References

M. H. Ashworth, Congruence and identical properties of modular forms, Diss. University of Oxford, 1968.

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

From Amiram Eldar, Jan 05 2025: (Start)

a(n) == 53 * sigma_11(n) (mod 729) for n == 2 (mod 3) (Kolberg, 1962).

a(n) == n^(-620) * sigma_1231(n) for n == 1 (mod 3) (Ashworth, 1968). (End)

Mathematica

a[n_] := Mod[RamanujanTau[n], 729]; Array[a, 100] (* Amiram Eldar, Jan 05 2025 *)

Prog

(PARI) a(n) = ramanujantau(n) % 729; \\ Amiram Eldar, Jan 05 2025

Crossrefs

Cf. A000594, A013959.

Sequence in context: A238322 A091553 A224491 * A005845 A183795 A335092

Adjacent sequences: A126827 A126828 A126829 * A126831 A126832 A126833

Keyword

nonn

Author

N. J. A. Sloane, Feb 25 2007

Status

approved