A126826 Ramanujan numbers (A000594) read mod 9.

1, 3, 0, 4, 6, 0, 5, 6, 0, 0, 3, 0, 8, 6, 0, 7, 0, 0, 2, 6, 0, 0, 6, 0, 7, 6, 0, 2, 3, 0, 8, 0, 0, 0, 3, 0, 2, 6, 0, 0, 6, 0, 5, 3, 0, 0, 3, 0, 3, 3, 0, 5, 0, 0, 0, 3, 0, 0, 6, 0, 5, 6, 0, 1, 3, 0, 8, 0, 0, 0, 0, 0, 2, 6, 0, 8, 6, 0, 5, 6, 0, 0, 3, 0, 0, 6, 0, 0, 0, 0, 4, 6, 0, 0, 3, 0, 5, 0, 0, 1, 3, 0, 8, 3, 0

Offset

1,2

Links

Table of n, a(n) for n=1..105.

R. P. Bambah and S. Chowla, A new congruence property of Ramanujan’s function tau(n), Bull. Amer. Math. Soc. 53 (1947), 768-769.

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) = n^2*sigma(n) mod 9. - Michel Marcus, Apr 25 2016

Mathematica

Mod[RamanujanTau@ #, 9] &@ Range@ 120 (* Michael De Vlieger, Apr 25 2016 *)

Prog

(PARI) a(n) = n^2*sigma(n) % 9; \\ Michel Marcus, Apr 26 2016

Crossrefs

Cf. A000203, A000594.

Sequence in context: A307383 A111486 A192878 * A231983 A231982 A198575

Adjacent sequences: A126823 A126824 A126825 * A126827 A126828 A126829

Keyword

nonn

Author

N. J. A. Sloane, Feb 25 2007

Status

approved