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%I #9 Jan 05 2025 01:06:06
%S 1,232,252,64,222,96,152,0,21,48,84,0,54,192,136,0,178,8,44,128,160,
%T 32,72,0,167,240,152,0,102,64,96,0,176,80,208,64,62,224,40,0,122,0,
%U 180,0,54,64,16,0,169,88,56,128,110,192,216,0,80,112,228,0,198,0,120,0,212,128,188
%N Ramanujan numbers (A000594) read mod 256.
%H Amiram Eldar, <a href="/A126818/b126818.txt">Table of n, a(n) for n = 1..10000</a>
%H George E. Andrews and Bruce C. Berndt, <a href="https://doi.org/10.1007/978-1-4614-3810-6_5">Ramanujan's Unpublished Manuscript on the Partition and Tau Functions</a>, in: Ramanujan's Lost Notebook, Part III, Springer, New York, NY, 2012.
%H R. P. Bambah and S. Chowla, <a href="https://doi.org/10.1112/jlms/s1-22.2.140">The Residue of Ramanujan's Function tau(n) to the Modulus 2^8</a>, Journal of the London Mathematical Society, Vol s1-22, No. 2 (1947), pp. 140-147.
%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) == sigma_11(n) (mod 256) for n odd (Bambah and Chowla, 1947; Andrews and Berndt, 2012, eq. (5.12.26), p. 118). - _Amiram Eldar_, Jan 05 2025
%t a[n_] := Mod[RamanujanTau[n], 256]; Array[a, 100] (* _Amiram Eldar_, Jan 05 2025 *)
%o (PARI) a(n) = ramanujantau(n) % 256; \\ _Amiram Eldar_, Jan 05 2025
%Y Cf. A000594, A013959.
%K nonn,changed
%O 1,2
%A _N. J. A. Sloane_, Feb 25 2007