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

Author

N. J. A. Sloane, Feb 25 2007

Keywords

• nonn

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.

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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