A126836 Ramanujan numbers (A000594) read mod 7.

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

Offset: 1

Author

N. J. A. Sloane, Feb 25 2007

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000
• R. P. Bambah, Ramanujan’s function tau(n)—A congruence property, Bull. Amer. Math. Soc. 53 (1947), 764-765.
• 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, A001158.

Cf. this sequence (mod 7^1), A126837 (mod 7^2), A126838 (mod 7^3).

Programs

Mathematica

Mod[RamanujanTau@ #, 7] &@ Range@ 120 (* Michael De Vlieger, Apr 25 2016 *)

PARI

a(n) = ramanujantau(n) % 7; \\ Amiram Eldar, Jan 05 2025

Formula

a(n) = n*sigma_3(n) mod 7. - Michel Marcus, Apr 25 2016