A126846 Ramanujan numbers (A000594) read mod 23^2.
1, 505, 252, 115, 69, 300, 184, 369, 92, 460, 322, 414, 459, 345, 460, 22, 161, 437, 483, 0, 345, 207, 254, 413, 162, 93, 116, 0, 344, 69, 229, 230, 207, 368, 0, 0, 207, 46, 346, 69, 160, 184, 138, 0, 0, 252, 459, 254, 139, 344, 368, 414, 253, 390, 0, 184, 46, 208, 71, 0
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
- Jean-Pierre Serre, Une interprétation des congruences relatives à la fonction tau de Ramanujan, Séminaire Delange-Pisot-Poitou, Théorie des nombres, Vol. 9, No. 1 (1967-1968), Talk no. 14, 17 p., section 4.5, page 14-11.
- 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], 529]; Array[a, 100] (* Amiram Eldar, Jan 05 2025 *)
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PARI
a(n) = ramanujantau(n) % 529; \\ Amiram Eldar, Jan 05 2025
Formula
a(p) == sigma_11(p) (mod 23^2) for prime p of the form u^2 + 23*v^2, u >= 1 (Serre, 1968). - Amiram Eldar, Jan 05 2025