A126812 Ramanujan numbers (A000594) read mod 4.

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

Offset

1,5

References

D. B. Lahiri, On Ramanujan's function tau(n) and divisor function sigma_k(n), I, Bulletin of the Calcutta Mathematical Society, Vol. 38 (1946), pp. 193-206; II, ibid., Vol. 39 (1947), pp. 33-51.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

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^2 * sigma_7(n) (mod 4) (Lahiri, 1946-1947). - Amiram Eldar, Jan 04 2025

Mathematica

Mod[#, 4] & /@ RamanujanTau@ Range@ 105 (* Michael De Vlieger, Nov 26 2017 *)

Prog

(PARI) A126812(n) = (ramanujantau(n)%4); \\ Antti Karttunen, Nov 26 2017

Crossrefs

Cf. A000594, A008442, A013955, A098108, A126813, A126814.

Sequence in context: A067618 A279255 A055029 * A008442 A338690 A343221

Adjacent sequences: A126809 A126810 A126811 * A126813 A126814 A126815

Keyword

nonn

Author

N. J. A. Sloane, Feb 25 2007

Status

approved