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

1,3

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.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000594, A000203, A098108, A105827, A126812, A126814.

Sequence in context: A351571 A308678 A184365 * A056141 A246004 A103688

Adjacent sequences: A126810 A126811 A126812 * A126814 A126815 A126816

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 25 2007

Status

approved