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Ramanujan numbers (A000594) read mod 5.
7

%I #20 Aug 24 2023 19:32:56

%S 1,1,2,3,0,2,1,0,2,0,2,1,2,1,0,1,1,2,0,0,2,2,2,0,0,2,0,3,0,0,2,1,4,1,

%T 0,1,1,0,4,0,2,2,2,1,0,2,1,2,3,0,2,1,2,0,0,0,0,0,0,0,2,2,2,3,0,4,1,3,

%U 4,0,2,0,2,1,0,0,2,4,0,0,1,2,2,1,0,2,0,0,0,0,2,1,4,1,0,2,1,3,4,0,2,2,2,0,0

%N Ramanujan numbers (A000594) read mod 5.

%D G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, AMS Chelsea Publishing, Providence, Rhode Island, 2002, pp. 166-167.

%H Seiichi Manyama, <a href="/A126832/b126832.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/S0002-9904-1947-08913-8">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*sigma(n) mod 5. - _Michel Marcus_, Apr 26 2016. See also the Hardy reference, p. 166, (10.5.2), with a proof. - _Wolfdieter Lang_, Feb 03 2017

%t Mod[RamanujanTau@ #, 5] & /@ Range@ 105 (* _Michael De Vlieger_, Apr 26 2016 *)

%o (Python)

%o from sympy import divisor_sigma

%o def A126832(n): return n*divisor_sigma(n)%5 # _Chai Wah Wu_, Aug 24 2023

%Y Cf. A000594, A064987.

%Y Cf. this sequence (mod 5^1), A126833 (mod 5^2), A126834 (mod 5^3), A126835 (mod 5^4).

%K nonn

%O 1,3

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