A126836 Ramanujan numbers (A000594) read mod 7.
1, 4, 0, 5, 0, 0, 0, 4, 2, 0, 1, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 4, 4, 0, 4, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 3, 4, 0, 0, 0, 0, 0, 2, 5, 0, 2, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0
Offset: 1
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..10000
- R. P. Bambah, Ramanujan’s function tau(n)—A congruence property, Bull. Amer. Math. Soc. 53 (1947), 764-765.
- 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.
Programs
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Mathematica
Mod[RamanujanTau@ #, 7] &@ Range@ 120 (* Michael De Vlieger, Apr 25 2016 *)
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PARI
a(n) = ramanujantau(n) % 7; \\ Amiram Eldar, Jan 05 2025
Formula
a(n) = n*sigma_3(n) mod 7. - Michel Marcus, Apr 25 2016