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

1,3

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George E. Andrews and Bruce C. Berndt, Ramanujan's Unpublished Manuscript on the Partition and Tau Functions, in: Ramanujan's Lost Notebook, Part III, Springer, New York, NY, 2012.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.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000594, A013957, A126832 (mod 5^1), this sequence (mod 5^2), A126834 (mod 5^3), A126835 (mod 5^4).

Sequence in context: A250445 A297996 A239692 * A138512 A053723 A201652

Adjacent sequences: A126830 A126831 A126832 * A126834 A126835 A126836

Keyword

nonn

Author

N. J. A. Sloane, Feb 25 2007

Status

approved