text: sqrt ( 2 * n ) as max length will be when the sum starts from 1 which follows the equation n ^ 2 - n - ( 2 * sum ) = 0
code: for ( int i = 2 ; i <= Math . Sqrt ( 2 * n ) ; i ++ ) { int a ; if ( ( 2 * n ) % i != 0 ) continue ; a = 2 * n ; a /= i ; a -= ( i - 1 ) ; if ( a % 2 != 0 ) continue ; a /= 2 ; if ( a > 0 ) { count ++ ; } } return count ; }