A140275 Total number of distinct solutions (modulo lcm(1,2,...,n)) of the system of congruences x == i (mod p(i)), i=1,2,...,n, where p is a permutation of order n.

1, 2, 5, 8, 32, 20, 120, 112, 172, 80, 1164, 312, 5160, 1852, 812, 432, 10168

Offset

1,2

Comments

The system of congruences x == i (mod p(i)) has the same solution as the system of congruences x == n-1-i (mod p'(i)) where p'=(p(n),p(n-1),...,p(1)). Therefore this sequence also gives the number of distinct solutions to the system of congruences x == -i (mod p(i)), i=1,2,...,n.

a(n) <= A140257(n).

Links

Table of n, a(n) for n=1..17.

Crossrefs

Cf. A003418, A138588, A140257.

Sequence in context: A066846 A304043 A290594 * A025533 A295970 A086809

Adjacent sequences: A140272 A140273 A140274 * A140276 A140277 A140278

Keyword

nonn,more

Author

Max Alekseyev, May 16 2008

Status

approved