A126825 Ramanujan numbers (A000594) read mod 3.

1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0

Offset: 1

Author

N. J. A. Sloane, Feb 25 2007

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• R. P. Bambah and S. Chowla, Congruence properties of Ramanujan’s function tau(n), Bull. Amer. Math. Soc. 53 (1947), 950-955.
• John A. Ewell, New representations of Ramanujan's tau function, Proc. Amer. Math. Soc. 128 (2000), 723-726.
• 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, A000203.

Programs

Maple

seq(modp(numtheory:-sigma(n),3)*(1-abs(mods(n-1,3))), n=1..105); # Peter Luschny, Apr 26 2016

Mathematica

Mod[RamanujanTau@ #, 3] & /@ Range@ 105 (* Michael De Vlieger, Apr 26 2016 *)

PARI

a(n) = ramanujantau(n) % 3; \\ Amiram Eldar, Jan 05 2025

Formula

a(4*n) = a(n) (see Corollary 2.2. p. 726 of Ewell link). - Michel Marcus, Dec 23 2012

a(n) = sigma(n) mod 3, for n coprime to 3. - Michel Marcus, Apr 26 2016