

A088922


Consider the n X n matrix with entries (i*j mod n), where i,j=0..n1; a(n) = rank of this matrix over the real numbers.


2



0, 1, 2, 3, 3, 5, 4, 6, 6, 7, 6, 10, 7, 9, 10, 11, 9, 13, 10, 14, 13, 13, 12, 18, 14, 15, 16, 18, 15, 21, 16, 20, 19, 19, 20, 25, 19, 21, 22, 26, 21, 27, 22, 26, 27, 25, 24, 32, 26, 29, 28, 30, 27, 33, 30, 34, 31, 31, 30, 40, 31, 33, 36, 37, 35, 39, 34, 38, 37, 41, 36, 46, 37, 39, 42, 42, 41, 45, 40, 48, 44, 43, 42, 52, 45, 45, 46, 50, 45, 55, 48, 50, 49, 49, 50, 58, 49, 53, 54, 57
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

Possibly related to Maillet's determinants.


LINKS

Table of n, a(n) for n=1..100.
Alexander Adam, Proof of the formula
Wikipedia, Maillet's determinant


FORMULA

Let n = Prod_{i>0} p_i^{m_i} be the prime factorization of n. Then a(n) = floor((n + 1)/2) + Prod_{i>0} (m_i + 1)  2.  Alexander Adam, Nov 10 2012
a(n) = A000005(n) + A110654(n)  2.


EXAMPLE

From Alexander Adam, Nov 10 2012, (Start)
a(2^m) = 2^(m1) + m  1.
Let p >= 3 be a prime number. Then a(p^m) = (p^m + 1) / 2 + m  1.
a(625000) = a(2^3*5^7) = 2^2*5^7 + 4 * 8  2 = 312530. (end)


MATHEMATICA

a[n_] := MatrixRank[Table[Table[Mod[i * j, n], {j, 0, n  1}], {i, 0, n  1}]]; Array[a, 100] (* Alexander Adam, Nov 10 2012 *)


PROG

(PARI) a(n) = matrank(matrix(n, n, i, j, (i*j)%n))


CROSSREFS

Cf. A218322, A055513, A203411, A000927.
Sequence in context: A088241 A163126 A304818 * A143092 A143089 A275314
Adjacent sequences: A088919 A088920 A088921 * A088923 A088924 A088925


KEYWORD

nonn


AUTHOR

Max Alekseyev, Dec 01 2003


STATUS

approved



