A126813 Ramanujan numbers (A000594) read mod 8.

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

Offset: 1

Author

N. J. A. Sloane, Feb 25 2007

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• R. P. Bambah, S. Chowla and H. Gupta, A congruence property of Ramanujan’s function tau(n), Bull. Amer. Math. Soc. 53 (1947), 766-767.
• 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, A098108, A105827, A126812, A126814.

Programs

Mathematica

Mod[RamanujanTau@ #, 8] &@ Range@ 120 (* Michael De Vlieger, Apr 25 2016 *)

PARI

A126813(n) = (ramanujantau(n)%8); \\ Antti Karttunen, Nov 26 2017

PARI

a(n)=my(e=valuation(n,2)); ramanujantau(2^e)*sigma(n>>e)%8 \\ Charles R Greathouse IV, Sep 09 2022

Formula

For all odd n, a(n) = sigma(n) mod 8 = A105827(n). - Michel Marcus, Apr 25 2016