cp's OEIS Frontend

d(m)*phi(m) is the product of f(p^k) = (p^k - p^(k-1))*(1+k), while sigma(m) is the product of g(p^k) = (p^(k+1)-1)/(p-1) taken over all prime powers p^k in the factorization of m. We have f(p^k) < g(p^k) for p=2 and k=1 or 2; f(p^k) = g(p^k) for p=3, k=1; and f(p^k) > g(p^k) in all other cases. Furthermore, f(2)/g(2) = 2/3 and f(2^2)/g(2^2) = 6/7, while f(p^k)/g(p^k) > f(p)/g(p) and for p > 7, f(p)/g(p) > 3/2. It easily follows that 1,3,14,42 are the only terms of this sequence. - Max Alekseyev, Feb 08 2010

Next term is greater than 3*10^9.

If n is a term of this sequence and gcd(10,n)=1 then 10*n is also in the sequence because reversal(10*n)=reversal(n); d(10)=phi(10) and both functions d & phi are multiplicative. No further terms up to 350000000.

a(5) > 10^12. - Giovanni Resta, Apr 25 2017