A126818 Ramanujan numbers (A000594) read mod 256.
1, 232, 252, 64, 222, 96, 152, 0, 21, 48, 84, 0, 54, 192, 136, 0, 178, 8, 44, 128, 160, 32, 72, 0, 167, 240, 152, 0, 102, 64, 96, 0, 176, 80, 208, 64, 62, 224, 40, 0, 122, 0, 180, 0, 54, 64, 16, 0, 169, 88, 56, 128, 110, 192, 216, 0, 80, 112, 228, 0, 198, 0, 120, 0, 212, 128, 188
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
- George E. Andrews and Bruce C. Berndt, Ramanujan's Unpublished Manuscript on the Partition and Tau Functions, in: Ramanujan's Lost Notebook, Part III, Springer, New York, NY, 2012.
- R. P. Bambah and S. Chowla, The Residue of Ramanujan's Function tau(n) to the Modulus 2^8, Journal of the London Mathematical Society, Vol s1-22, No. 2 (1947), pp. 140-147.
- 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], 256]; Array[a, 100] (* Amiram Eldar, Jan 05 2025 *)
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PARI
a(n) = ramanujantau(n) % 256; \\ Amiram Eldar, Jan 05 2025
Formula
a(n) == sigma_11(n) (mod 256) for n odd (Bambah and Chowla, 1947; Andrews and Berndt, 2012, eq. (5.12.26), p. 118). - Amiram Eldar, Jan 05 2025