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A126828 Ramanujan numbers (A000594) read mod 81. 0

%I #10 Apr 26 2016 10:34:40

%S 1,57,9,67,51,27,23,78,0,72,12,36,35,15,54,70,45,0,38,15,45,36,69,54,

%T 61,51,0,2,3,0,17,9,27,54,39,0,74,60,72,9,6,54,41,75,0,45,75,63,21,75,

%U 0,77,54,0,45,12,18,9,24,54,50,78,0,37,3,0,62,18,54,36,18,0,65,6,63,35,33,54

%N Ramanujan numbers (A000594) read mod 81.

%H R. P. Bambah and S. Chowla, <a href="http://dx.doi.org/10.1090/S0002-9904-1947-08913-8">Congruence properties of Ramanujan’s function tau(n)</a>, Bull. Amer. Math. Soc. 53 (1947), 950-955.

%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+k)*sigma_7(n) with k=0 if gcd(n,3)=1 and k=9 if gcd(n,3)=2. - _Michel Marcus_, Apr 26 2016

%t Mod[RamanujanTau@ #, 81] & /@ Range@ 78 (* _Michael De Vlieger_, Apr 26 2016 *)

%Y Cf. A000594, A013955.

%K nonn

%O 1,2

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

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