A126828 Ramanujan numbers (A000594) read mod 81.

1, 57, 9, 67, 51, 27, 23, 78, 0, 72, 12, 36, 35, 15, 54, 70, 45, 0, 38, 15, 45, 36, 69, 54, 61, 51, 0, 2, 3, 0, 17, 9, 27, 54, 39, 0, 74, 60, 72, 9, 6, 54, 41, 75, 0, 45, 75, 63, 21, 75, 0, 77, 54, 0, 45, 12, 18, 9, 24, 54, 50, 78, 0, 37, 3, 0, 62, 18, 54, 36, 18, 0, 65, 6, 63, 35, 33, 54

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.
• 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, A013955.

Programs

Mathematica

Mod[RamanujanTau@ #, 81] & /@ Range@ 78 (* Michael De Vlieger, Apr 26 2016 *)

PARI

a(n) = ramanujantau(n) % 81; \\ Amiram Eldar, Jan 05 2025

Formula

a(n) = (n^2+k)*sigma_7(n) with k=0 if gcd(n,3)=1 and k=9 if gcd(n,3)=2. - Michel Marcus, Apr 26 2016