Today's submission to OEIS:

5, 13, 37, 109, 2917, 19131877, 57395629, 16210220612075905069

They are the primes of the form 4×3n+1, for n up to 39 (after which I got lazy and stopped, but it may be possible to find larger ones without specialized algorithms).

To my knowledge T. Venkataraman was the first to consider these primes; he showed in 1975 that multiplying them by 3 produces perfect totient numbers.

Venkataraman, T. (1975). "Perfect totient number". The Mathematics Student 43: 178. MR0447089.

ETA: The 1972 Math. Comp. reference in A005537 is a little older, but less specific, so I think the title of this post is still appropriate.