A126814 Ramanujan numbers (A000594) read mod 16.
1, 8, 12, 0, 14, 0, 8, 0, 5, 0, 4, 0, 6, 0, 8, 0, 2, 8, 12, 0, 0, 0, 8, 0, 7, 0, 8, 0, 6, 0, 0, 0, 0, 0, 0, 0, 14, 0, 8, 0, 10, 0, 4, 0, 6, 0, 0, 0, 9, 8, 8, 0, 14, 0, 8, 0, 0, 0, 4, 0, 6, 0, 8, 0, 4, 0, 12, 0, 0, 0, 8, 0, 10, 0, 4, 0, 0, 0, 0, 0, 9, 0, 12, 0, 12, 0, 8, 0, 10, 0, 0, 0, 0, 0, 8, 0, 2, 8, 4, 0
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
- J. M. Rushforth, Congruence properties of the partition function and associated functions, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 48, No. 3 (1952), pp. 402-413.
- 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], 16]; Array[a, 100] (* Amiram Eldar, Jan 04 2025 *)
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PARI
a(n) = ramanujantau(n) % 16; \\ Amiram Eldar, Jan 04 2025
Formula
a(n) == n^3 * sigma(n) (mod 16) (Rushforth, 1952). - Amiram Eldar, Jan 04 2025