A020479 Number of noninvertible 2 X 2 matrices over Z/nZ (determinant is a divisor of 0).

10, 33, 160, 145, 1008, 385, 2560, 2673, 7120, 1441, 16128, 2353, 26320, 27585, 40960, 5185, 81648, 7201, 113920, 97713, 155056, 12673, 258048, 90625, 299728, 216513, 421120, 25201, 671760, 30721, 655360, 552321, 866320, 532945, 1306368, 51985

Offset

2,1

Links

Table of n, a(n) for n=2..37.

Formula

a(n) seems to be divisible by n. - Ralf Stephan, Sep 01 2003 [This is true and can be easily proven from the formula below and from the multiplicative formula for A000252(n). - Amiram Eldar, Aug 03 2024]

a(n) = n^4 - A000252(n). - T. D. Noe, Jan 16 2006

Mathematica

f[p_, e_] := (p - 1)^2*(p + 1)*p^(4*e - 3); a[n_] := n^4 - Times @@ f @@@ FactorInteger[n]; Array[a, 36, 2] (* Amiram Eldar, Aug 03 2024 *)

Prog

(PARI) a(n) = {my(f = factor(n), p = f[, 1], e=f[, 2]); n^4 - prod(k = 1, #p, (p[k] - 1)^2*(p[k] + 1)*p[k]^(4*e[k] - 3)); } \\ Amiram Eldar, Aug 03 2024

Crossrefs

Cf. A000252.

Sequence in context: A373129 A004638 A211033 * A219818 A264251 A140866

Adjacent sequences: A020476 A020477 A020478 * A020480 A020481 A020482

Keyword

nonn

Author

David W. Wilson

Status

approved