On a theorem of Zumkeller related to twin primes

Question

Let $\{p_1,p_2\}$ be a twin prime pair, $\phi(n)$ denote Euler's totient function and $\sigma(n)$ the sum-of-divisors function. Reinhard Zumkeller proved in 2002 that

$$ \phi(p_2) = \sigma(p_1). $$

However I cannot find Zumkeller's paper proving this fact. Can anyone kindly point me to a link where I can read his Theorem?

Answer 1

There's not much to prove, certainly not enough for a paper. $\phi(p_2)=p_2-1$, as for any prime, and $\sigma(p_1)=p_1+1$, as for any prime; since they're twin primes, $p_2-1=p_1+1$.