Sequence Involving Relative Primality

[Leroy Quet]

Let r_m = product[k] * sum[1/k], where both the product and sum are
over those positive integers, k, where k <= m and GCD(k,m) = 1.

({r_m} is sequence A056855 of the On-Line Encyclopedia of Integer 
Sequences.)

Let phi(m) be the number of positive integers <= m and relatively
prime to m.

Does (m phi(m)) divide (2 r_m) for all positive integers, m ?

Thanks,
Leroy Quet