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Ramanujan numbers (A000594) read mod 16384.
1

%I #9 Jan 05 2025 01:07:38

%S 1,16360,252,14912,4830,10336,16024,2560,1045,15152,10324,5888,12086,

%T 8640,4744,4096,8114,7688,11820,896,7584,14368,14664,6144,10663,4848,

%U 6552,5632,5222,832,11616,0,12976,1872,14288,1856,9534,11232,14632,11264,2938,14592

%N Ramanujan numbers (A000594) read mod 16384.

%D Oddmund Kolberg, Congruences for Ramanujan's Function ̈tau(n), Univ. Bergen Årbok Naturvit Rekke, No. 11, 1962.

%H Amiram Eldar, <a href="/A126824/b126824.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) == 705 * sigma_11(n) (mod 16384) for n == 7 (mod 8) (Kolberg, 1962). - _Amiram Eldar_, Jan 05 2025

%t a[n_] := Mod[RamanujanTau[n], 16384]; Array[a, 100] (* _Amiram Eldar_, Jan 05 2025 *)

%o (PARI) a(n) = ramanujantau(n) % 16384; \\ _Amiram Eldar_, Jan 05 2025

%Y Cf. A000594, A013959.

%K nonn

%O 1,2

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