computational challenge related to very odd sequences

[Pieter Moree]

Dear seqfans,

Let phi denote the Euler totient function.
For d an odd number, let ord_2(d) denote the order of
2 modulo d (smallest k>=1 such that 2^k=1(mod d).

Consider the function
i_2(n)=sum_{d|n}phi(d)/ord_2(d).

Let S be the set of odd integers n such that ord_2(n) is
odd, and n has at least one prime divisor p such that
p^2 does not divide n (e.g. 7^{14}*73, 31*151).

For an integer n in S we have i_2(n) is odd.
Let i_2(S)={m: i_2(n)=m for some n in S}

Under the Generalized Riemann Hypothesis it can be shown that
each number in i_2(S) has an infinite preimage.

All odd integers <=800 except possibly
13,29,37,53,61,149,181,229,293,373,461,541,757,773 are in i_2(S).

I would be very happy to learn if somebody can find an integer
n in S for which i_2(n) assumes one of the exceptional values
listed above.

This is related to the very odd sequences introduced by Pelikan
in the 70's which have applications to coding theory.

Regards,
Pieter Moree