Nonexistence of odd perfect numbers of a certain form

Write N = p(alpha)q(1)(2 beta 1)... q(k)(2 beta k) where p, q(1),..., q(k) are distinct odd primes and p equivalent to alpha equivalent to 1 4). An odd perfect number, if it exists, must have this form. McDaniel proved in 1970 that N is not perfect if all beta(i) are congruent to 1 (mod 3). Hagis and McDaniel proved in 1975 that N is not perfect if all beta(i) are congruent to 17 (mod 35). We prove that N is not perfect if all beta(i) are congruent to 32 (mod 65). We also show that N is not perfect if all beta(i) are congruent to 2 (mod 5) and either 7 vertical bar N or 3 vertical bar N. This is related to a result of Iannucci and Sorli, who proved in 2003 that N is not perfect if each beta(i) is congruent either to 2 (mod 5) or 1 (mod 3) and 3 vertical bar N.