cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 41-43 of 43 results.

A065552 a(n) = floor(sqrt(phi(10^n)*sigma(10^n) + 10^(3*n))).

Original entry on oeis.org

1, 32, 1004, 31637, 1000048, 31622932, 1000000496, 31622778176, 1000000004990, 31622776617479, 1000000000049975, 31622776601841868, 1000000000000499938, 31622776601685374362, 1000000000000004999847, 31622776601683809131135, 1000000000000000049999618, 31622776601683793478102215
Offset: 0

Views

Author

Labos Elemer, Nov 13 2001

Keywords

Comments

Similar results are obtained if the cube is replaced with other odd powers.

Crossrefs

Cf. A000010, A000203, A062354, A065655, A065656.

Programs

  • Mathematica
    a[n_]:=Floor[Sqrt[EulerPhi[10^n]DivisorSigma[1,10^n]+10^(3n)]]; Array[a,17,0] (* Stefano Spezia, Mar 23 2023 *)

Extensions

a(0) = 1 prepended by, a(11)-a(15) corrected by, and a(16)-a(17) from Stefano Spezia, Mar 23 2023

A364770 Number of conjugacy classes in the group GL(4,Z_n).

Original entry on oeis.org

1, 14, 78, 306, 620, 1092, 2394, 5808, 7164, 8680, 14630, 23868, 28548, 33516, 48360
Offset: 1

Views

Author

Robin Visser, Aug 06 2023

Keywords

Crossrefs

Cf. A062354, A086768.

Programs

  • Magma
    [Nclasses(GeneralLinearGroup(4, ResidueClassRing(n))) : n in [2..15]];

Formula

For a prime p : a(p) = p*(p^3 - 1).

A364847 Number of conjugacy classes in the group SL(2, Z_n), up to conjugacy in GL(2, Z_n).

Original entry on oeis.org

1, 3, 5, 8, 7, 15, 9, 20, 17, 21, 13, 40, 15, 27, 35, 44, 19, 51, 21, 56, 45, 39, 25, 100, 37, 45, 53, 72, 31, 105, 33, 92, 65, 57, 63, 136, 39, 63, 75, 140, 43, 135, 45, 104, 119, 75, 49, 220, 65, 111, 95, 120, 55, 159, 91, 180, 105, 93, 61, 280, 63, 99, 153, 188, 105, 195, 69
Offset: 1

Views

Author

Robin Visser, Aug 10 2023

Keywords

Comments

Here two matrices A, B in SL(2, Z_n) are in the same conjugacy class if P^-1*A*P = B for some matrix P in GL(2, Z_n).

Crossrefs

Cf. A062354, A065501.

Programs

  • Magma
    [#[c[3] : c in Classes(GL(2,ResidueClassRing(n))) | Determinant(c[3]) eq 1] : n in [2..50]];

Formula

For an odd prime p : a(p) = p + 2.
Previous Showing 41-43 of 43 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.