A140275 - OEIS

%I #9 Dec 07 2019 22:29:39

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

%N 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.

%C 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.

%C a(n) <= A140257(n).

%Y Cf. A003418, A138588, A140257.

%K nonn,more

%O 1,2

%A _Max Alekseyev_, May 16 2008