(In reply to
computer solution by Charlie)
https://oeis.org/A175169
Numbers n such that n divides the sum of digits of 2^n. 1, 2, 5, 70
Not quite the same but any others in our set would be in this sequence.
And as I promised in my comment, I was surprised to see another example.
Edited on May 27, 2016, 4:42 pm

Posted by Jer
on 20160527 16:42:04 