A126833 - OEIS

%I #14 Jan 05 2025 01:10:32

%S 1,1,2,3,5,2,6,5,7,5,12,6,12,6,10,11,16,7,20,15,12,12,22,10,0,12,20,

%T 18,5,10,7,21,24,16,5,21,11,20,24,0,17,12,17,11,10,22,21,22,18,0,7,11,

%U 2,20,10,5,15,5,10,5,12,7,17,18,10,24,16,23,19,5,22,10,22,11,0,10,22,24,5,5

%N Ramanujan numbers (A000594) read mod 25.

%H Seiichi Manyama, <a href="/A126833/b126833.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Ramanujan's Unpublished Manuscript on the Partition and Tau Functions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 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 * sigma_9(n) (mod 25) (Andrews and Berndt, 2012, eq. (5.4.2), p. 98). - _Amiram Eldar_, Jan 04 2025

%t a[n_] := Mod[RamanujanTau[n], 25]; Array[a, 100] (* _Amiram Eldar_, Jan 04 2025 *)

%o (PARI) a(n) = ramanujantau(n) % 25; \\ _Amiram Eldar_, Jan 04 2025

%Y Cf. A000594, A013957, A126832 (mod 5^1), this sequence (mod 5^2), A126834 (mod 5^3), A126835 (mod 5^4).

%K nonn

%O 1,3

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