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A005353 Number of 2 X 2 matrices with entries mod n and nonzero determinant.
(Formerly M4254)
5
0, 6, 48, 168, 480, 966, 2016, 3360, 5616, 8550, 13200, 17832, 26208, 34566, 45840, 59520, 78336, 95526, 123120, 147240, 181776, 219846, 267168, 307488, 372000, 433446, 505440, 580776, 682080, 762150, 892800, 999936, 1138368, 1284486 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
T. Brenner, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
FORMULA
a(n) = n^4 - A020478(n).
For prime n, a(n) = (n^2-1)(n-1)n. - T. D. Noe, Jan 12 2006
MATHEMATICA
Table[cnt=0; Do[m={{a, b}, {c, d}}; If[Det[m, Modulus->p] > 0, cnt++ ], {a, 0, p-1}, {b, 0, p-1}, {c, 0, p-1}, {d, 0, p-1}]; cnt, {p, 37}] (* T. D. Noe, Jan 12 2006 *)
f[p_, e_] := p^(2*e - 1)*(p^(e + 1) + p^e - 1); a[1] = 0; a[n_] := n^4 - Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 31 2023 *)
PROG
(PARI) a(n) = {my(f = factor(n), p, e); n^4 - prod(i = 1, #f~, p = f[i, 1]; e = f[i, 2]; p^(2*e - 1)*(p^(e + 1) + p^e - 1)); } \\ Amiram Eldar, Oct 31 2023
CROSSREFS
Sequence in context: A244726 A335384 A331668 * A047927 A059238 A371067
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from T. D. Noe, Jan 12 2006
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)