A126837 Ramanujan numbers (A000594) read mod 7^2.
1, 25, 7, 47, 28, 28, 14, 4, 37, 14, 22, 35, 21, 7, 0, 31, 28, 43, 0, 42, 0, 11, 46, 28, 32, 35, 28, 21, 23, 0, 0, 31, 7, 14, 0, 24, 46, 0, 0, 14, 14, 0, 37, 5, 7, 23, 42, 21, 0, 16, 0, 7, 36, 14, 28, 7, 0, 36, 42, 0, 14, 0, 28, 7, 0, 28, 15, 42, 28, 0, 2, 1, 14, 23, 28, 0, 14, 0, 39, 35, 46
Offset: 1
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..10000
- Oddmund Kolberg, Note on Ramanujan's Function tau(n), Mathematica Scandinavica, Vol. 10 (1962), pp. 171-172; alternative link.
- 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
a[n_] := Mod[RamanujanTau[n], 49]; Array[a, 100] (* Amiram Eldar, Jan 05 2025 *)
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PARI
a(n) = ramanujantau(n) % 49; \\ Amiram Eldar, Jan 05 2025
Formula
a(n) == n * sigma_9(n) (mod 7^2) if Legendre symbol (n,7) = A175629(n) = -1 (Kolberg, 1962). - Amiram Eldar, Jan 05 2025