A126837 Ramanujan numbers (A000594) read mod 7^2.

1, 25, 7, 47, 28, 28, 14, 4, 37, 14, 22, 35, 21, 7, 0, 31, 28, 43, 0, 42, 0, 11, 46, 28, 32, 35, 28, 21, 23, 0, 0, 31, 7, 14, 0, 24, 46, 0, 0, 14, 14, 0, 37, 5, 7, 23, 42, 21, 0, 16, 0, 7, 36, 14, 28, 7, 0, 36, 42, 0, 14, 0, 28, 7, 0, 28, 15, 42, 28, 0, 2, 1, 14, 23, 28, 0, 14, 0, 39, 35, 46

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Oddmund Kolberg, Note on Ramanujan's Function tau(n), Mathematica Scandinavica, Vol. 10 (1962), pp. 171-172; alternative link.

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 7^2) if Legendre symbol (n,7) = A175629(n) = -1 (Kolberg, 1962). - Amiram Eldar, Jan 05 2025

Mathematica

a[n_] := Mod[RamanujanTau[n], 49]; Array[a, 100] (* Amiram Eldar, Jan 05 2025 *)

Prog

(PARI) a(n) = ramanujantau(n) % 49; \\ Amiram Eldar, Jan 05 2025

Crossrefs

Cf. A000594, A013957, A126836 (mod 7^1), this sequence (mod 7^2), A126838 (mod 7^3).

Sequence in context: A091736 A245631 A243092 * A248583 A080203 A040605

Adjacent sequences: A126834 A126835 A126836 * A126838 A126839 A126840

Keyword

nonn

Author

N. J. A. Sloane, Feb 25 2007

Status

approved