A126832 Ramanujan numbers (A000594) read mod 5.

1, 1, 2, 3, 0, 2, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 1, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 3, 0, 0, 2, 1, 4, 1, 0, 1, 1, 0, 4, 0, 2, 2, 2, 1, 0, 2, 1, 2, 3, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 3, 0, 4, 1, 3, 4, 0, 2, 0, 2, 1, 0, 0, 2, 4, 0, 0, 1, 2, 2, 1, 0, 2, 0, 0, 0, 0, 2, 1, 4, 1, 0, 2, 1, 3, 4, 0, 2, 2, 2, 0, 0

Offset: 1

Author

N. J. A. Sloane, Feb 25 2007

Keywords

• nonn

References

• G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, AMS Chelsea Publishing, Providence, Rhode Island, 2002, pp. 166-167.

Links

• Seiichi Manyama, 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. A000203, A000594, A064987.

Cf. this sequence (mod 5^1), A126833 (mod 5^2), A126834 (mod 5^3), A126835 (mod 5^4).

Programs

Mathematica

Mod[RamanujanTau@ #, 5] & /@ Range@ 105 (* Michael De Vlieger, Apr 26 2016 *)

PARI

a(n) = n*sigma(n) % 5; \\ Amiram Eldar, Jan 05 2025

Python

from sympy import divisor_sigma
def A126832(n): return n*divisor_sigma(n)%5 # Chai Wah Wu, Aug 24 2023

Formula

a(n) = n*sigma(n) mod 5. - Michel Marcus, Apr 26 2016. See also the Hardy reference, p. 166, (10.5.2), with a proof. - Wolfdieter Lang, Feb 03 2017