A126833 Ramanujan numbers (A000594) read mod 25.

1, 1, 2, 3, 5, 2, 6, 5, 7, 5, 12, 6, 12, 6, 10, 11, 16, 7, 20, 15, 12, 12, 22, 10, 0, 12, 20, 18, 5, 10, 7, 21, 24, 16, 5, 21, 11, 20, 24, 0, 17, 12, 17, 11, 10, 22, 21, 22, 18, 0, 7, 11, 2, 20, 10, 5, 15, 5, 10, 5, 12, 7, 17, 18, 10, 24, 16, 23, 19, 5, 22, 10, 22, 11, 0, 10, 22, 24, 5, 5

Offset: 1

Author

N. J. A. Sloane, Feb 25 2007

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000
• George E. Andrews and Bruce C. Berndt, Ramanujan's Unpublished Manuscript on the Partition and Tau Functions, in: Ramanujan's Lost Notebook, Part III, Springer, New York, NY, 2012.
• 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, A013957, A126832 (mod 5^1), this sequence (mod 5^2), A126834 (mod 5^3), A126835 (mod 5^4).

Programs

Mathematica

a[n_] := Mod[RamanujanTau[n], 25]; Array[a, 100] (* Amiram Eldar, Jan 04 2025 *)

PARI

a(n) = ramanujantau(n) % 25; \\ Amiram Eldar, Jan 04 2025

Formula

a(n) == n * sigma_9(n) (mod 25) (Andrews and Berndt, 2012, eq. (5.4.2), p. 98). - Amiram Eldar, Jan 04 2025