A364847 - OEIS

A364847

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

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

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OFFSET

1,2

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).

LINKS

Table of n, a(n) for n=1..67.

FORMULA

For an odd prime p: a(p) = p + 2.

Conjecture: a(n) = Sum_{d|n} d*A060594(n/d). - Ridouane Oudra, Feb 16 2026

PROG

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