computational challenge related to very odd sequences

Don Reble djr at
Sat Jun 26 00:35:46 CEST 2004

> 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).

> i_2(n)=sum_{d|n}phi(d)/ord_2(d).
> Let i_2(S)={m: i_2(n)=m for some n in S}

Hmm... you've given that name to two different things.
Still, I think I know what you mean.

> 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).

> find an integer n in S for which i_2(n) assumes one of the exceptional
> values listed above.


i_2(63)=13,      i_2(1191)=29,   i_2(1649)=37,   i_2(585)=53,
i_2(3913)=61,    i_2(7695)=149,  i_2(13143)=181, i_2(73143)=229,
i_2(4599)=293,   i_2(29319)=373, i_2(25025)=461, i_2(77121)=541,
i_2(299831)=757, i_2(64305)=773.

But that looks too easy. Did I get something wrong?

Don Reble       djr at

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