A295071 Number of von Neumann regular elements in the ring of 2 X 2 matrices over Z_n.

1, 16, 81, 169, 625, 1296, 2401, 2113, 4753, 10000, 14641, 13689, 28561, 38416, 50625, 29185, 83521, 76048, 130321, 105625, 194481, 234256, 279841, 171153, 318001, 456976, 338257, 405769, 707281, 810000, 923521, 430081, 1185921, 1336336

Offset

1,2

Comments

An element a of a ring is called a von Neumann regular element if there exists an x such that a = axa.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..41

Mathematica

G[A_, n_] := Reduce[A == A.{{x, y}, {z, t}}.A, Modulus -> n];
H[n_] := Sum[If[G[{{a, b}, {c, d}}, n] === False, 0, 1], {a, n}, {b, n}, {c, n}, {d, n}];
Table[H[n], {n, 2, 14}]

Crossrefs

Sequence in context: A346484 A065771 A320965 * A223951 A041490 A096020

Adjacent sequences: A295068 A295069 A295070 * A295072 A295073 A295074

Keyword

nonn,mult

Author

José María Grau Ribas, Nov 13 2017

Extensions

a(19) inserted by José María Grau Ribas, Feb 13 2018

More terms from Robert G. Wilson v, Feb 14 2018

Status

approved