A126815 Ramanujan numbers (A000594) read mod 32.

1, 8, 28, 0, 30, 0, 24, 0, 21, 16, 20, 0, 22, 0, 8, 0, 18, 8, 12, 0, 0, 0, 8, 0, 7, 16, 24, 0, 6, 0, 0, 0, 16, 16, 16, 0, 30, 0, 8, 0, 26, 0, 20, 0, 22, 0, 16, 0, 9, 24, 24, 0, 14, 0, 24, 0, 16, 16, 4, 0, 6, 0, 24, 0, 20, 0, 28, 0, 0, 0, 24, 0, 26, 16, 4, 0, 0, 0, 16, 0, 9, 16, 12, 0, 28, 0, 8, 0

Offset

1,2

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.

Formula

a(n) == n^3 * sigma_5(n) (mod 32) (Rushforth, 1952). - Amiram Eldar, Jan 05 2025

Mathematica

a[n_] := Mod[RamanujanTau[n], 32]; Array[a, 100] (* Amiram Eldar, Jan 05 2025 *)

Prog

(PARI) a(n) = ramanujantau(n) % 32; \\ Amiram Eldar, Jan 05 2025

Crossrefs

Cf. A000594, A001160.

Sequence in context: A027454 A229114 A088029 * A053619 A272259 A112663

Adjacent sequences: A126812 A126813 A126814 * A126816 A126817 A126818

Keyword

nonn

Author

N. J. A. Sloane, Feb 25 2007

Status

approved