On the sum of divisors function

Abstract. The following assertion is proved. Let \(Q_1,Q_2\) be odd primes, \(A_{Q_1,Q_2}(x)\) be the number of those \(n \leq x\) for which \(Q_1\nmid\sigma(n),Q_2\nmid\sigma(n+1)\) simultaneously hold. Then \(A_{Q_1,Q_2}(x) \geq \frac{cx}{(\log x)^5}\), if \(x>X_0\). \(c\), \(X_0\) are positive constants.