A126832 Ramanujan numbers (A000594) read mod 5.
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, 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, 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
Offset: 1
Keywords
References
- G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, AMS Chelsea Publishing, Providence, Rhode Island, 2002, pp. 166-167.
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..10000
- R. P. Bambah and S. Chowla, Congruence properties of Ramanujan’s function tau(n), Bull. Amer. Math. Soc. 53 (1947), 950-955.
- H. P. F. Swinnerton-Dyer, On l-adic representations and congruences for coefficients of modular forms, pp. 1-55 of Modular Functions of One Variable III (Antwerp 1972), Lect. Notes Math., 350, 1973.
Crossrefs
Programs
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Mathematica
Mod[RamanujanTau@ #, 5] & /@ Range@ 105 (* Michael De Vlieger, Apr 26 2016 *)
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PARI
a(n) = n*sigma(n) % 5; \\ Amiram Eldar, Jan 05 2025
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Python
from sympy import divisor_sigma def A126832(n): return n*divisor_sigma(n)%5 # Chai Wah Wu, Aug 24 2023
Formula
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