A126845 - OEIS

%I #9 Jan 05 2025 01:10:58

%S 1,22,22,0,0,1,0,1,0,0,0,0,22,0,0,22,0,0,0,0,0,0,1,22,1,1,1,0,22,0,22,

%T 0,0,0,0,0,0,0,1,0,22,0,0,0,0,22,22,1,1,22,0,0,0,22,0,0,0,1,2,0,0,1,0,

%U 1,0,0,0,0,22,0,22,0,22,0,22,0,0,22,0,0,22,1,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0

%N Ramanujan numbers (A000594) read mod 23.

%D G. H. Hardy, Ramanujan, Twelve Lectures on Subjects Suggested by His Life and Work, Cambridge, 1940, p. 166.

%H Amiram Eldar, <a href="/A126845/b126845.txt">Table of n, a(n) for n = 1..10000</a>

%H H. P. F. Swinnerton-Dyer, <a href="http://dx.doi.org/10.1007/978-3-540-37802-0_1">On l-adic representations and congruences for coefficients of modular forms</a>, pp. 1-55 of Modular Functions of One Variable III (Antwerp 1972), Lect. Notes Math., 350, 1973.

%F a(n) = 0 if Legendre symbol (n,23) = A011586(n) = -1 (Hardy, 1940). - _Amiram Eldar_, Jan 04 2025

%t a[n_] := Mod[RamanujanTau[n], 23]; Array[a, 100] (* _Amiram Eldar_, Jan 04 2025 *)

%o (PARI) a(n) = ramanujantau(n) % 23; \\ _Amiram Eldar_, Jan 04 2025

%Y Cf. A000594, A011586.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Feb 25 2007