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

1,7

Comments

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

Links

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

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.

Formula

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

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 *)

Crossrefs

Cf. A000594, A000203.

Sequence in context: A293814 A045837 A319687 * A045833 A117896 A356735

Adjacent sequences: A126822 A126823 A126824 * A126826 A126827 A126828

Keyword

nonn

Author

N. J. A. Sloane, Feb 25 2007

Status

approved