A126839 -id:A126839 - cp's OEIS frontend

A126840 Ramanujan numbers (A000594) read mod 11^2.

1, 97, 10, 101, 111, 2, 75, 22, 97, 119, 34, 42, 37, 15, 21, 18, 20, 92, 110, 79, 24, 31, 76, 99, 73, 80, 93, 73, 99, 101, 73, 8, 98, 4, 97, 117, 102, 22, 7, 22, 113, 29, 27, 46, 119, 112, 85, 59, 19, 63, 79, 107, 5, 67, 23, 77, 11, 44, 82, 64, 23, 63, 15, 91, 114, 68, 59, 84, 34

Offset: 1

N. J. A. Sloane, Feb 25 2007

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000
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.

Cf. A000594, A126839 (mod 11^1), this sequence (mod 11^2), A126841 (mod 11^3).

a[n_] := Mod[RamanujanTau[n], 121]; Array[a, 100] (* Amiram Eldar, Jan 05 2025 *)

a(n) = ramanujantau(n) % 121; \\ Amiram Eldar, Jan 05 2025

A126841 Ramanujan numbers (A000594) read mod 11^3.

Original entry on oeis.org

1, 1307, 252, 1190, 837, 607, 559, 627, 823, 1208, 881, 405, 1247, 1225, 626, 865, 625, 213, 110, 442, 1113, 152, 1286, 946, 73, 685, 456, 1041, 1067, 948, 194, 855, 1066, 972, 702, 1085, 586, 22, 128, 385, 597, 1239, 269, 893, 724, 1080, 932, 1027, 1229, 910, 442

Offset: 1

N. J. A. Sloane, Feb 25 2007

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000
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.

Cf. A000594, A126839 (mod 11^1), A126840 (mod 11^2), this sequence (mod 11^3).

a[n_] := Mod[RamanujanTau[n], 1331]; Array[a, 100] (* Amiram Eldar, Jan 05 2025 *)

a(n) = ramanujantau(n) % 1331; \\ Amiram Eldar, Jan 05 2025

A289633 a(n) = 6 * Sum_{d|n} d * A110163(d).

Original entry on oeis.org

-1440, 319680, -73733760, 17014849920, -3926422987200, 906079372542720, -209091033317387520, 48250806224270918400, -11134577434408058898720, 2569466177758810678838400, -592941804710481150566417280, 136829971461225574971638023680

Offset: 1

Seiichi Manyama, Jul 08 2017

sign

			G.f.: -1440*q + 319680*q^2 - 73733760*q^3 + 17014849920*q^4 - 3926422987200*q^5 + ...
a(1) = 6 * (1 * A110163(1)) = -1440,
a(2) = 6 * (1 * A110163(1) + 2 * A110163(2)) = 319680,
a(3) = 6 * (1 * A110163(1) + 3 * A110163(3)) = -73733760.

Seiichi Manyama, Table of n, a(n) for n = 1..422
Ken Ono, The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-series, CBMS Regional Conference Series in Mathematics, vol. 102, American Mathematical Society, Providence, RI, 2004.

Cf. A000594, A110163, A126839 (A000594(n) mod 11), A289636.

a(n) == A000594(n) mod 11.

a(n) ~ 6 * (-1)^n * exp(Pi*sqrt(3)*n). - Vaclav Kotesovec, Jul 09 2017

cp's OEIS Frontend

A126840 Ramanujan numbers (A000594) read mod 11^2.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

A126841 Ramanujan numbers (A000594) read mod 11^3.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

A289633 a(n) = 6 * Sum_{d|n} d * A110163(d).

Views

Author

Keywords

Examples

Links

Crossrefs

Formula