cp's OEIS Frontend

Subsequence of A236693. Proof: if n is in this sequence, then 2^phi(n) - 1 is divisible by n and 2^sigma(n) - 1 is divisible by 2^phi(n) - 1. Therefore, 2^sigma(n) == 1 (mod n) and n is in A236693. - Jinyuan Wang, Mar 13 2020

Rotkiewicz defined these numbers and found the first 6 terms that are semiprimes (6, 14, 15, 35, 65, 119, and 377).

Křížek et al. named these numbers Rotkiewicz numbers, and proved that the following criteria are equivalent to the definition:

1) Numbers k such that c^sigma(k) == 1 (mod k) for all numbers c such that gcd(c, k) = 1.

2) Numbers k such that lambda(k) | sigma(k) where lambda is the Carmichael lambda function (A002322).

They also proved that:

1) If M(p) = 2^p-1 is a Mersenne prime (A000668) then 2^(p-2)*M(p) is a term.

2) If n is a term and, 2^k is the largest power of 2 that divides sigma(n), and F(m) = 2^(2^m) + 1 is a Fermat prime not dividing n such that m <= log_2(k+1) then n*F(m) is also a term.