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%I #18 Jan 05 2025 01:07:49
%S 1,3,0,4,6,0,5,6,0,0,3,0,8,6,0,7,0,0,2,6,0,0,6,0,7,6,0,2,3,0,8,0,0,0,
%T 3,0,2,6,0,0,6,0,5,3,0,0,3,0,3,3,0,5,0,0,0,3,0,0,6,0,5,6,0,1,3,0,8,0,
%U 0,0,0,0,2,6,0,8,6,0,5,6,0,0,3,0,0,6,0,0,0,0,4,6,0,0,3,0,5,0,0,1,3,0,8,3,0
%N Ramanujan numbers (A000594) read mod 9.
%H Amiram Eldar, <a href="/A126826/b126826.txt">Table of n, a(n) for n = 1..10000</a>
%H R. P. Bambah and S. Chowla, <a href="http://dx.doi.org/10.1090/S0002-9904-1947-08871-6">A new congruence property of Ramanujan’s function tau(n)</a>, Bull. Amer. Math. Soc. 53 (1947), 768-769.
%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) = n^2*sigma(n) mod 9. - _Michel Marcus_, Apr 25 2016
%t Mod[RamanujanTau@ #, 9] &@ Range@ 120 (* _Michael De Vlieger_, Apr 25 2016 *)
%o (PARI) a(n) = n^2*sigma(n) % 9; \\ _Michel Marcus_, Apr 26 2016
%Y Cf. A000203, A000594.
%K nonn,changed
%O 1,2
%A _N. J. A. Sloane_, Feb 25 2007