A126813 - OEIS

%I #19 Sep 09 2022 18:22:09

%S 1,0,4,0,6,0,0,0,5,0,4,0,6,0,0,0,2,0,4,0,0,0,0,0,7,0,0,0,6,0,0,0,0,0,

%T 0,0,6,0,0,0,2,0,4,0,6,0,0,0,1,0,0,0,6,0,0,0,0,0,4,0,6,0,0,0,4,0,4,0,

%U 0,0,0,0,2,0,4,0,0,0,0,0,1,0,4,0,4,0,0,0,2,0,0,0,0,0,0,0,2,0,4,0,6,0,0,0,0

%N Ramanujan numbers (A000594) read mod 8.

%H Antti Karttunen, <a href="/A126813/b126813.txt">Table of n, a(n) for n = 1..65537</a>

%H R. P. Bambah, S. Chowla and H. Gupta, <a href="http://dx.doi.org/10.1090/S0002-9904-1947-08870-4">A congruence property of Ramanujan’s function tau(n)</a>, Bull. Amer. Math. Soc. 53 (1947), 766-767.

%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 For all odd n, a(n) = sigma(n) mod 8 = A105827(n). - _Michel Marcus_, Apr 25 2016

%t Mod[RamanujanTau@ #, 8] &@ Range@ 120 (* _Michael De Vlieger_, Apr 25 2016 *)

%o (PARI) A126813(n) = (ramanujantau(n)%8); \\ _Antti Karttunen_, Nov 26 2017

%o (PARI) a(n)=my(e=valuation(n,2)); ramanujantau(2^e)*sigma(n>>e)%8 \\ _Charles R Greathouse IV_, Sep 09 2022

%Y Cf. A000594, A000203, A098108, A105827, A126812, A126814.

%K nonn,easy

%O 1,3

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