Let denotes the sum of the positive divisors of the positive integer and be the Euler’s totient function(,page25). Cleary, divides if is a prime. Then, the question is there a composite that divides ? Considering this problem Yang-Gao Chen and Jin-Hui Fang  have proved that , where as usual is the number of distinct prime factors of. and , .We devoted the study of this problem where we prove that every in is odd and that , from which it follows that for any composite in the least prime factors is . Also, we obtained lower bounds for and for any with , which improves the result of  in some cases.
Al-Aidroos, Hussain Abdulkader
"On n Satisfying, n Dividing φ(n)σ(n)+1,"
Hadhramout University Journal of Natural & Applied Sciences: Vol. 17:
2, Article 5.
Available at: https://digitalcommons.aaru.edu.jo/huj_nas/vol17/iss2/5