4 is a member of the sequence since Sum_{j=1..4} j^phi(j) = 1^phi(1) + 2^phi(2) + 3^phi(3) + 4^phi(4) = 1^1 + 2^1 + 3^2 + 4^2 = 28 which is divisible by 4.
MAPLE
with(numtheory); ListA227429:=proc(q) local i, n;
for n from 1 to q do if add(i^phi(i), i=1..n) mod n=0 then print(n);
